Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States

Fast Generation of GHZ-like States Using Collective-Spin XYZ Model

The Greenberger-Horne-Zeilinger (GHZ) state is a key resource for quantum information processing and quantum metrology. The atomic GHZ state can be generated by one-axis twisting (OAT) interaction H_{OAT}=χJ_{z}^{2} with χ the interaction strength, but it requires a long evolution time χt=π/2 and is thus seriously influenced by decoherence and losses. Here we propose a three-body collective-spin XYZ model which creates a GHZ-like state in a very short timescale χt∼lnN/N for N particles. We show that this model can be effectively produced by applying Floquet driving to an original OAT Hamiltonian. Compared with the ideal GHZ state, the GHZ-like state generated using our model can maintain similar metrological properties reaching the Heisenberg-limited scaling, and it shows better robustness to decoherence and particle losses. This Letter opens the avenue for generating GHZ-like states with a large particle number, which holds great potential for the study of macroscopic quantum effects and for applications in quantum metrology and quantum information.

Ultracompact Single-Photon Sources of Linearly Polarized Vortex Beams

Ultracompact chip-integrated single-photon sources of collimated beams with polarization-encoded states are crucial for integrated quantum technologies. However, most of currently available single-photon sources rely on external bulky optical components to shape the polarization and phase front of emitted photon beams. Efficient integration of quantum emitters with beam shaping and polarization encoding functionalities remains so far elusive. Here, ultracompact single-photon sources of linearly polarized vortex beams based on chip-integrated quantum emitter-coupled metasurfaces are presented, which are meticulously designed by fully exploiting the potential of nanobrick-arrayed metasurfaces. The authors first demonstrate on-chip single-photon generation of high-purity linearly polarized vortex beams with prescribed topological charges of 0, - 1, and +1. The multiplexing of single-photon emission channels with orthogonal linear polarizations carrying different topological charges are further realized and their entanglement is demonstarated. The work illustrates the potential and feasibility of ultracompact quantum emitter-coupled metasurfaces as a new quantum optics platform for realizing chip-integrated high-dimensional single-photon sources.

Phase estimation of definite photon number states by using quantum circuits

We propose a method to map the conventional optical interferometry setup into quantum circuits. The unknown phase shift inside a Mach-Zehnder interferometer in the presence of photon loss is estimated by simulating the quantum circuits. For this aim, we use the Bayesian approach in which the likelihood functions are needed, and they are obtained by simulating the appropriate quantum circuits. The precision of four different definite photon-number states of light, which all possess six photons, is compared. The measurement scheme that we have considered is counting the number of photons detected after the final beam splitter of the interferometer, and photon loss is modeled by using fictitious beam splitters in the arms of the interferometer. Our results indicate that three of the four definite photon-number states considered can have better precision than the standard interferometry limit whenever the photon loss rate is in a specific range. In addition, the Fisher information for the four definite photon-number states in the setup is also estimated to check the optimality of the chosen measurement scheme.

Squeezed Superradiance Enables Robust Entanglement-Enhanced Metrology Even with Highly Imperfect Readout

Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.

Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology

Permitting a more precise measurement to physical quantities than the classical limit by using quantum resources, quantum metrology holds a promise in developing many revolutionary technologies. However, the noise-induced decoherence forces its superiority to disappear, which is called no-go theorem of noisy quantum metrology and constrains its application. We propose a scheme to overcome the no-go theorem by Floquet engineering. It is found that, by applying a periodic driving on the atoms of the Ramsey spectroscopy, the ultimate sensitivity to measure their frequency characterized by quantum Fisher information returns to the ideal t^{2} scaling with the encoding time whenever a Floquet bound state is formed by the system consisting of each driven atom and its local noise. Combining with the optimal control, this mechanism also allows us to retrieve the ideal Heisenberg-limit scaling with the atom number N. Our result gives an efficient way to avoid the no-go theorem of noisy quantum metrology and to realize high-precision measurements.

Stark Localization as a Resource for Weak-Field Sensing with Super-Heisenberg Precision

Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function at all energy scales, a phenomenon known as Stark localization. Here, we show that Stark systems can be used as a probe for the precise measurement of gradient fields, particularly in the weak-field regime where most sensors do not operate optimally. In the extended phase, Stark probes achieve super-Heisenberg precision, which is well beyond most of the known quantum sensing schemes. In the localized phase, the precision drops in a universal way showing fast convergence to the thermodynamic limit. For single-particle probes, we show that quantum-enhanced sensitivity, with super-Heisenberg precision, can be achieved through a simple position measurement for all the eigenstates across the entire spectrum. For such probes, we have identified several critical exponents of the Stark localization transition and established their relationship. Thermal fluctuations, whose universal behavior is identified, reduce the precision from super-Heisenberg to Heisenberg, still outperforming classical sensors. Multiparticle interacting probes also achieve super-Heisenberg scaling in their extended phase, which shows even further enhancement near the transition point. Quantum-enhanced sensitivity is still achievable even when state preparation time is included in resource analysis.

Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of O(ε^{-1}), the proposed algorithm can efficiently estimate any parameter in the N-qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N-qubit Hamiltonian H into noninteracting patches and learns H using a quantum-enhanced divide-and-conquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog(ε^{-1}) experiments. In contrast, the best existing algorithms require O(ε^{-2}) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

Strong Quantum Metrological Limit from Many-Body Physics

Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that does not come without a price. The exceptional time overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here, we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to characterize the metrological potential of quantum resource states during their preparation. Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit in a generic many-body lattice system with bounded one-site energy. It enables us to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology, and brings an interesting connection between many-body quantum dynamics and quantum metrology.

Approaching optimal entangling collective measurements on quantum computing platforms

Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer better sensitivity, per resource, than what can be achieved classically. However, to reach the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks, collective measurements, which generate entanglement between multiple copies of the quantum state, are necessary. Here, we experimentally demonstrate theoretically optimal single- and two-copy collective measurements for simultaneously estimating two non-commuting qubit rotations. This allows us to implement quantum-enhanced sensing, for which the metrological gain persists for high levels of decoherence, and to draw fundamental insights about the interpretation of the uncertainty principle. We implement our optimal measurements on superconducting, trapped-ion and photonic systems, providing an indication of how future quantum-enhanced sensing networks may look.

Error-Mitigated Quantum Metrology via Virtual Purification

Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our result is the first demonstration to reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise.

Quantum metrology with imperfect measurements

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections—with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

The effects of detection noise on quantum metrology performances have not been rigorously investigated yet. Here, the authors fill this gap by generalising the quantum Fisher information to the case of noisy readout, and showing the consequences the imperfect measurements bring.

Inference-Based Quantum Sensing

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω(log^{3}(n)/δ^{2}). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

Preparation and Analysis of Two-Dimensional Four-Qubit Entangled States with Photon Polarization and Spatial Path

Entanglement states serve as the central resource for a number of important applications in quantum information science, including quantum key distribution, quantum precision measurement, and quantum computing. In pursuit of more promising applications, efforts have been made to generate entangled states with more qubits. However, the efficient creation of a high-fidelity multiparticle entanglement remains an outstanding challenge due to the difficulty that increases exponentially with the number of particles. We design an interferometer that is capable of coupling the polarization and spatial paths of photons and prepare 2-D four-qubit GHZ entanglement states. Using quantum state tomography, entanglement witness, and the violation of Ardehali inequality against local realism, the properties of the prepared 2-D four-qubit entangled state are analyzed. The experimental results show that the prepared four-photon system is an entangled state with high fidelity.

Sequential Measurements for Quantum-Enhanced Magnetometry in Spin Chain Probes

Quantum sensors outperform their classical counterparts in their estimation precision, given the same amount of resources. So far, quantum-enhanced sensitivity has been achieved by exploiting the superposition principle. This enhancement has been obtained for particular forms of entangled states, adaptive measurement basis change, critical many-body systems, and steady state of periodically driven systems. Here, we introduce a different approach to obtain quantum-enhanced sensitivity in a many-body probe through utilizing the nature of quantum measurement and its subsequent wave function collapse without demanding prior entanglement. Our protocol consists of a sequence of local measurements, without reinitialization, performed regularly during the evolution of a many-body probe. As the number of sequences increases, the sensing precision is enhanced beyond the standard limit, reaching the Heisenberg bound asymptotically. The benefits of the protocol are multifold as it uses a product initial state and avoids complex initialization (e.g., prior entangled states or critical ground states) and allows for remote quantum sensing.

An elementary quantum network of entangled optical atomic clocks

Optical atomic clocks are our most precise tools to measure time and frequency^1-3. Precision frequency comparisons between clocks in separate locations enable one to probe the space-time variation of fundamental constants^4,5 and the properties of dark matter^6,7, to perform geodesy^8-10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory-the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances^11-16, comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link^17,18 to entangle two ⁸⁸Sr⁺ ions separated by a macroscopic distance¹⁹ (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly [Formula: see text], the value predicted for the Heisenberg limit. Today's optical clocks are typically limited by dephasing of the probe laser²⁰; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques^20-22. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes²³, to other species of trapped particles or-through local operations-to larger entangled systems.

Thermodynamic Signatures of Genuinely Multipartite Entanglement

The theory of bipartite entanglement shares profound similarities with thermodynamics. In this Letter we extend this connection to multipartite quantum systems where entanglement appears in different forms with genuine entanglement being the most exotic one. We propose thermodynamic quantities that capture a signature of genuineness in multipartite entangled states. Instead of entropy, these quantities are defined in terms of energy-particularly the difference between global and local extractable works (ergotropies) that can be stored in quantum batteries. Some of these quantities suffice as faithful measures of genuineness and to some extent distinguish different classes of genuinely entangled states. Along with scrutinizing properties of these measures we compare them with the other existing genuine measures, and argue that they can serve the purpose in a better sense. Furthermore, the generality of our approach allows us to define suitable functions of ergotropies capturing the signature of k nonseparability that characterizes qualitatively different manifestations of entanglement in multipartite systems.

Quantum-enhanced radiometry via approximate quantum error correction

Quantum sensing based on exotic quantum states is appealing for practical metrology applications and fundamental studies. However, these quantum states are vulnerable to noise and the resulting quantum enhancement is weakened in practice. Here, we experimentally demonstrate a quantum-enhanced sensing scheme with a bosonic probe, by exploring the large Hilbert space of the bosonic mode and developing both the approximate quantum error correction and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches 9.1 × 10⁻⁴ Hz^−1/2 when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing, but also stimulating further efforts on bosonic quantum technologies.

Exotic quantum states can be advantageous for sensing, but are very fragile, so that some form of quantum error correction is needed. Here, the authors show how approximate QEC helps overcoming decoherence due to noise when measuring the excitation population of a receiver mode in a superconducting circuit.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28}  dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously

We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress the insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the advantage of the optimal simultaneous estimation scheme amounts to a constant factor improvement when compared with schemes where each phase is estimated separately, which is contrary to widely cited results claiming a better precision scaling in terms of the number of phases involved.

Enhanced Parameter Estimation with Periodically Driven Quantum Probe

I propose a quantum metrology protocol for measuring frequencies and weak forces based on a periodic modulating quantum Jahn–Teller system composed of a single spin and two bosonic modes. I show that, in the first order of the frequency drive, the time-independent effective Hamiltonian describes spin-dependent interaction between the two bosonic modes. In the limit of high-frequency drive and low bosonic frequency, the quantum Jahn–Teller system exhibits critical behavior which can be used for high-precision quantum estimation. A major advantage of the scheme is the robustness of the system against spin decoherence, which allows it to perform parameter estimation with measurement time not limited by spin dephasing.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

Global Sensing and Its Impact for Quantum Many-Body Probes with Criticality

Quantum sensing is one of the key areas that exemplify the superiority of quantum technologies. Nonetheless, most quantum sensing protocols operate efficiently only when the unknown parameters vary within a very narrow region, i.e., local sensing. Here, we provide a systematic formulation for quantifying the precision of a probe for multiparameter global sensing when there is no prior information about the parameters. In many-body probes, in which extra tunable parameters exist, our protocol can tune the performance for harnessing the quantum criticality over arbitrarily large sensing intervals. For the single-parameter sensing, our protocol optimizes a control field such that an Ising probe is tuned to always operate around its criticality. This significantly enhances the performance of the probe even when the interval of interest is so large that the precision is bounded by the standard limit. For the multiparameter case, our protocol optimizes the control fields such that the probe operates at the most efficient point along its critical line. Finally, it is shown that even a simple magnetization measurement significantly benefits from our global sensing protocol.

Metrological Detection of Multipartite Entanglement from Young Diagrams

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and k-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients.

Ultra-high dynamic range quantum measurement retaining its sensitivity

Quantum sensors are highly sensitive since they capitalise on fragile quantum properties such as coherence, while enabling ultra-high spatial resolution. For sensing, the crux is to minimise the measurement uncertainty in a chosen range within a given time. However, basic quantum sensing protocols cannot simultaneously achieve both a high sensitivity and a large range. Here, we demonstrate a non-adaptive algorithm for increasing this range, in principle without limit, for alternating-current field sensing, while being able to get arbitrarily close to the best possible sensitivity. Therefore, it outperforms the standard measurement concept in both sensitivity and range. Also, we explore this algorithm thoroughly by simulation, and discuss the T⁻² scaling that this algorithm approaches in the coherent regime, as opposed to the T^−1/2 of the standard measurement. The same algorithm can be applied to any modulo-limited sensor.

Usually, quantum sensing protocols impose a trade-off between sensitivity and maximum range. Here, the authors demonstrate a non-adaptive algorithm for quantum sensors to measure AC fields with a large range for which the loss in sensitivity is negligible.

Practical quantum-enhanced receivers for classical communication

Communication is an integral part of human life. Today, optical pulses are the preferred information carriers for long-distance communication. The exponential growth in data leads to a “capacity crunch” in the underlying physical systems. One of the possible methods to deter the exponential growth of physical resources for communication is to use quantum, rather than classical measurement at the receiver. Quantum measurement improves the energy efficiency of optical communication protocols by enabling discrimination of optical coherent states with the discrimination error rate below the shot-noise limit. In this review article, the authors focus on quantum receivers that can be practically implemented at the current state of technology, first and foremost displacement-based receivers. The authors present the experimentalist view on the progress in quantum-enhanced receivers and discuss their potential.

Prospects and challenges for squeezing-enhanced optical atomic clocks

Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.

Bayesian Optimal Control of Greenberger-Horne-Zeilinger States in Rydberg Lattices

The ability to prepare nonclassical states in a robust manner is essential for quantum sensors beyond the standard quantum limit. We demonstrate that Bayesian optimal control is capable of finding control pulses that drive trapped Rydberg atoms into highly entangled Greenberger-Horne-Zeilinger states. The control sequences have a physically intuitive functionality based on the quasi-integrability of the Ising dynamics. They can be constructed in laboratory experiments, resulting in preparation times that scale very favorably with the system size.

Manipulating Complex Hybrid Entanglement and Testing Multipartite Bell Inequalities in a Superconducting Circuit

Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is 8.381±0.038, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.

Deterministic control of photonic de Broglie waves using coherence optics

Photonic de Broglie waves offer a unique property of quantum mechanics satisfying the complementarity between the particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the nonclassical feature of photon bunching has been newly interpreted using the pure wave nature of coherence optics [Sci. Rep. 10, 7,309 (2020)], paving the road to unconditionally secured classical key distribution [Sci. Rep. 10, 11,687 (2020)]. Here, deterministic photonic de Broglie waves are presented in a coherence regime to uncover new insights in both fundamental quantum physics and potential applications of coherence-quantum metrology.

Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits

Multipartite entangled states are crucial for numerous applications in quantum information science. However, the generation and verification of multipartite entanglement on fully controllable and scalable quantum platforms remains an outstanding challenge. We report the deterministic generation of an 18-qubit Greenberger-Horne-Zeilinger (GHZ) state and multicomponent atomic Schrödinger cat states of up to 20 qubits on a quantum processor, which features 20 superconducting qubits, also referred to as artificial atoms, interconnected by a bus resonator. By engineering a one-axis twisting Hamiltonian, the system of qubits, once initialized, coherently evolves to multicomponent atomic Schrödinger cat states-that is, superpositions of atomic coherent states including the GHZ state-at specific time intervals as expected. Our approach on a solid-state platform should not only stimulate interest in exploring the fundamental physics of quantum many-body systems, but also enable the development of applications in practical quantum metrology and quantum information processing.

Berry-Hannay relation in nonlinear optomechanics

We address the quantum-classical comparison of phase measurements in optomechanics in the general framework of Berry phases for composite systems. While the relation between Berry phase and Hannay angle has been proven for a large set of quadratic Hamiltonians, such correspondence has not been shown so far in the case of non-linear interactions (e.g. when three or more operators are involved). Remarkably, considering the full optomechanical interaction we recover the aforementioned mathematical relation with the Hannay angle obtained from classical equations of motion. Our results link at a fundamental level previous proposals to measure decoherence, such as the one expressed by Marshall et al., with the no-go theorem shown by Armata et al., which provides boundaries to understand the quantum-to-classical transition in optomechanics.

Quantum Logic Spectroscopy with Ions in Thermal Motion

A mixed-species geometric phase gate has been proposed for implementing quantum logic spectroscopy on trapped ions, which combines probe and information transfer from the spectroscopy to the logic ion in a single pulse. We experimentally realize this method, show how it can be applied as a technique for identifying transitions in currently intractable atoms or molecules, demonstrate its reduced temperature sensitivity, and observe quantum-enhanced frequency sensitivity when it is applied to multi-ion chains. Potential applications include improved readout of trapped-ion clocks and simplified error syndrome measurements for quantum error correction.

Heralded Generation of Macroscopic Superposition States in a Spinor Bose-Einstein Condensate

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.

Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three ^{176}Lu^{+} ions. Microwave spectroscopy between hyperfine states in the ^{3}D_{1} level is used to characterize differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the ∼10^{-17} level relative to the ^{1}S_{0}↔^{3}D_{1} optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ)=8.2×10^{-17}/sqrt[τ].

Multi-outcome homodyne detection in a coherent-state light interferometer

The Cramér-Rao bound plays a central role in both classical and quantum parameter estimation, but finding the observable and the resulting inversion estimator that saturates this bound remains an open issue for general multi-outcome measurements. Here we consider multi-outcome homodyne detection in a coherent-light Mach-Zehnder interferometer and construct a family of inversion estimators that almost saturate the Cramér-Rao bound over the whole range of phase interval. This provides a clue on constructing optimal inversion estimators for phase estimation and other parameter estimation in any multi-outcome measurement.

Improved Test of Local Lorentz Invariance from a Deterministic Preparation of Entangled States

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.

Experimental learning of quantum states

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling limits our ability to characterize and simulate the evolution of arbitrary states to systems, with no more than a few qubits. However, from a computational learning theory perspective, it can be shown that quantum states can be approximately learned using a number of measurements growing linearly with the number of qubits. Here, we experimentally demonstrate this linear scaling in optical systems with up to 6 qubits. Our results highlight the power of the computational learning theory to investigate quantum information, provide the first experimental demonstration that quantum states can be "probably approximately learned" with access to a number of copies of the state that scales linearly with the number of qubits, and pave the way to probing quantum states at new, larger scales.

Quantum Effects in a Mechanically Modulated Single-Photon Emitter

Recent observation of quantum emitters in monolayers of hexagonal boron nitride (h-BN) has provided a novel platform for optomechanical experiments where the single-photon emitters can couple to the motion of a freely suspended h-BN membrane. Here, we propose a scheme where the electronic degree of freedom (d.o.f.) of an embedded color center is coupled to the motion of the hosting h-BN resonator via dispersive forces. We show that the coupling of membrane vibrations to the electronic d.o.f. of the emitter can reach the strong regime. By suitable driving of a three-level Λ-system composed of two spin d.o.f. in the electronic ground state as well as an isolated excited state of the emitter, a multiple electromagnetically induced transparency spectrum becomes available. The experimental feasibility of the efficient vibrational ground-state cooling of the membrane via quantum interference effects in the two-color drive scheme is numerically confirmed. More interestingly, the emission spectrum of the defect exhibits a frequency comb with frequency spacings as small as the fundamental vibrational mode, which finds applications in high-precision spectroscopy.

Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom

Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. Here, we use dysprosium atoms-the most magnetic element in its ground state-to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J = 8. We drive coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states-close to the Heisenberg limit 2J = 16-and an intrinsic fragility to environmental noise.

Maximal quantum Fisher information for phase estimation without initial parity

Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interferometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.

Toward Heisenberg-Limited Rabi Spectroscopy

The use of entangled states was shown to improve the fundamental limits of spectroscopy to beyond the standard-quantum limit. Here, rather than probing the free evolution of the phase of an entangled state with respect to a local oscillator, we probe the evolution of an initially separable two-atom register under an Ising spin Hamiltonian with a transverse field. The resulting correlated spin-rotation spectrum is twice as narrow as that of an uncorrelated rotation. We implement this ideally Heisenberg-limited Rabi spectroscopy scheme on the optical-clock electric-quadrupole transition of ^{88}Sr^{+} using a two-ion crystal. We further show that depending on the initial state, correlated rotation can occur in two orthogonal subspaces of the full Hilbert space, yielding entanglement-enhanced spectroscopy of either the average transition frequency of the two ions or their difference from the mean frequency. The use of correlated spin rotations can potentially lead to new paths for clock stability improvement.

Entanglement loss in molecular quantum-dot qubits due to interaction with the environment

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunković-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.

Quantum metrology with quantum-chaotic sensors

Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems, such as precessing spins or harmonic oscillators prepared in non-classical states. Here we show that large benefits can be drawn from rendering integrable quantum sensors chaotic, both in terms of achievable sensitivity as well as robustness to noise, while avoiding the challenge of preparing and protecting large-scale entanglement. We apply the method to spin-precession magnetometry and show in particular that the sensitivity of state-of-the-art magnetometers can be further enhanced by subjecting the spin-precession to non-linear kicks that renders the dynamics chaotic.

Enhanced sensing using quantum systems generally relies on preparation of highly non-classical states, such as entangled or squeezed states. Here the authors propose a different approach, based on hypersensitivity of quantum-chaotic dynamics with respect to parameters of the system.

Achieving the Heisenberg limit in quantum metrology using quantum error correction

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.

Hybrid Integration of Solid-State Quantum Emitters on a Silicon Photonic Chip

Scalable quantum photonic systems require efficient single photon sources coupled to integrated photonic devices. Solid-state quantum emitters can generate single photons with high efficiency, while silicon photonic circuits can manipulate them in an integrated device structure. Combining these two material platforms could, therefore, significantly increase the complexity of integrated quantum photonic devices. Here, we demonstrate hybrid integration of solid-state quantum emitters to a silicon photonic device. We develop a pick-and-place technique that can position epitaxially grown InAs/InP quantum dots emitting at telecom wavelengths on a silicon photonic chip deterministically with nanoscale precision. We employ an adiabatic tapering approach to transfer the emission from the quantum dots to the waveguide with high efficiency. We also incorporate an on-chip silicon-photonic beamsplitter to perform a Hanbury-Brown and Twiss measurement. Our approach could enable integration of precharacterized III-V quantum photonic devices into large-scale photonic structures to enable complex devices composed of many emitters and photons.

Rebuilding of destroyed spin squeezing in noisy environments

We investigate the process of spin squeezing in a ferromagnetic dipolar spin-1 Bose-Einstein condensate under the driven one-axis twisting scheme, with emphasis on the detrimental effect of noisy environments (stray magnetic fields) which completely destroy the spin squeezing. By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments, we faithfully reconstruct the spin squeezing process under realistic experimental conditions. Our noise-resistant method is ready to be employed to generate the spin squeezed state in a dipolar spin-1 Bose-Einstein condensate and paves a feasible way to the Heisenberg-limit quantum metrology.

Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade

We report on the first experimental realization of the controlled-not (cnot) quantum gate and entanglement for two individual atoms of different isotopes and demonstrate a negligible cross talk between two atom qubits. The experiment is based on a strong Rydberg blockade for ^{87}Rb and ^{85}Rb atoms confined in two single-atom optical traps separated by 3.8  μm. The raw fidelities of the cnot gate and entanglement are 0.73±0.01 and 0.59±0.03, respectively, without any corrections for atom loss or trace loss. Our work has applications for simulations of many-body systems with multispecies interactions, for quantum computing, and for quantum metrology.