Detection of entanglement in asymmetric quantum networks and multipartite quantum steering

Activation of Einstein-Podolsky-Rosen steering sharing with unsharp nonlocal measurements

Einstein-Podolsky-Rosen (EPR) steering is commonly shared among multiple observers by utilizing unsharp measurements. Nevertheless, their usage is restricted to local measurements and does not encompass all nonlocal measurement-based cases. In this work, a method for finding beneficial local measurement settings has been expanded to include nonlocal measurement cases. This method is applicable for any bipartite state and offers benefits even in scenarios with a high number of measurement settings. Using the Greenberger-Horne-Zeilinger state as an illustration, we show that employing unsharp nonlocal measurements can activate the phenomenon of steering sharing in contrast to using local measurements. Furthermore, our findings demonstrate that nonlocal measurements with unequal strength possess a greater activation capability compared to those with equal strength. Our activation method generates fresh concepts for conservation and recycling quantum resources.

Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems

Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.

Self-Testing with Dishonest Parties and Device-Independent Entanglement Certification in Quantum Communication Networks

We consider the task of device-independent quantum state certification in a network where some of the nodes may collude and act dishonestly. We introduce the paradigm of self-testing with dishonest parties and provide a certification protocol for the Greenberger-Horne-Zeilinger state in this framework, together with robust statements about the fidelity of the shared state. We extend our results to the cluster scenario, where many subgroups of parties may collude. Our findings provide a new operational motivation for the strong definition of genuine multipartite nonlocality originally introduced by Svetlichny.

Observation of Non-Markovian Evolution of Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering is a type of characteristic nonlocal correlation and provides an important resource in quantum information tasks, especially in view of its asymmetric property. Although plenty of works on EPR steering have been reported, the study of non-Markovian evolution of EPR steering, in which the interactions between the quantum system and surrounding environment are taken into consideration, still lacks intuitive experimental evidence. Here, we experimentally observe the non-Markovian evolution of EPR steering including its sudden death and revival processes, during which the degree of memory effect plays a key role in the recovery of steering. Additionally, a strict unsteerable feature is sufficiently verified during the non-Markovian evolution within multisetting measurements. This Letter, revealing the whole evolution of EPR steering under the non-Markovian process, provides incisive insight into the applications of EPR steering in quantum open systems.

Dynamics of multipartite quantum steering for different types of decoherence channels

Multipartite quantum steering, a unique resource for asymmetric quantum network information tasks, is very fragile to the inevitable decoherence, which makes it useless for practical purposes. It is thus of importance to understand how it decays in the presence of noise channels. We study the dynamic behaviors of genuine tripartite steering, reduced bipartite steering, and collective steering of a generalized three-qubit W state when only one qubit interacts independently with the amplitude damping channel (ADC), phase damping channel (PDC) or depolarizing channel (DC). Our results provide the region of decoherence strength and state parameters that each type of steering can survive. The results show that these steering correlations decay the slowest in PDC and some non-maximally entangled states more robust than the maximally entangled ones. Unlike entanglement and Bell nonlocality, the thresholds of decoherence strength that reduced bipartite steering and collective steering can survive depend on the steering direction. In addition, we find that not only one party can be steered by a group system, but also two parties can be steered by a single system. There is a trade-off between the monogamy relation involving one steered party and two steered parties. Our work provides comprehensive information about the effect of decoherence on multipartite quantum steering, which will help to realize quantum information processing tasks in the presence of noise environments.

Deterministic manipulation of steering between distant quantum network nodes

Multipartite Einstein-Podolsky-Rosen (EPR) steering is a key resource in a quantum network. Although EPR steering between spatially separated regions of ultracold atomic systems has been observed, deterministic manipulation of steering between distant quantum network nodes is required for a secure quantum communication network. Here, we propose a feasible scheme to deterministically generate, store, and manipulate one-way EPR steering between distant atomic cells by a cavity-enhanced quantum memory approach. While optical cavities effectively suppress the unavoidable noises in electromagnetically induced transparency, three atomic cells are in a strong Greenberger-Horne-Zeilinger state by faithfully storing three spatially separated entangled optical modes. In this way, the strong quantum correlation of atomic cells guarantees one-to-two node EPR steering is achieved, and can perserve the stored EPR steering in these quantum nodes. Furthermore, the steerability can be actively manipulated by the temperature of the atomic cell. This scheme provides the direct reference for experimental implementation for one-way multipartite steerable states, which enables an asymmetric quantum network protocol.

Witnessing multi-observer steering on both sides simultaneously via weak measurements

The quantum steering as an intermediate form of quantum correlations, has various peculiarities differing from the Bell nonlocality and the quantum entanglement. In a specific scenario, each side of the observer shares one of the two entangled qubits, steering can be witnessed simultaneously between any two observers from different sides by performing weak or projective measurements successively, with independently chosen and unbiased inputs. Here, we demonstrate this steering scenario experimentally to simultaneously witness quartic Einstein-Podolsky-Rosen steerings of two successive observers between each side with the entangled pair with a state fidelity of 97.6% compared with a maximally-entangled one.

Detecting Tripartite Steering via Quantum Entanglement

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.

Complete classification of steerability under local filters and its relation with measurement incompatibility

Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

The study of quantum steering has both foundational and practical interest. Here, the authors show that transformability of a steerable resource into another via local filtering at the trusted party is determined by whether they have the same steering equivalent observables (SEO).

Quantum Steering in Two- and Three-Mode ??-Symmetric Systems

We consider two PT-symmetric models, consisting of two or three single-mode cavities. In both models, the cavities are coupled to each other by linear interactions, forming a linear chain. Additionally, the first and last of such cavities interact with an environment. Since the models are PT-symmetric, they are described by non-Hermitian Hamiltonians that, for a specific range of system parameters, possess real eigenvalues. We show that in the models considered in the article, the steering generation process strongly depends on the coupling strengths and rates of the gains/losses in energy. Moreover, we find the values of parameters describing the system for which the steering appears.

Network Quantum Steering

The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.

Frequency and polarization emission properties of a photon-pair source based on a photonic crystal fiber

In this work, we experimentally demonstrate a photon-pair source with correlations in the frequency and polarization degrees of freedom. We base our source on the spontaneous four-wave mixing (SFWM) process in a photonic crystal fiber. We show theoretically that the two-photon state is the coherent superposition of up to six distinct SFWM processes, each corresponding to a distinct combination of polarizations for the four waves involved and giving rise to an energy-conserving pair of peaks. Our experimental measurements, both in terms of single and coincidence counts, confirm the presence of these pairs of peaks, while we also present related numerical simulations with excellent experiment-theory agreement. We explicitly show how the pump frequency and polarization may be used to effectively control the signal-idler photon-pair properties, defining which of the six processes can participate in the overall two-photon state and at which optical frequencies. We analyze the signal-idler correlations in frequency and polarization, and in terms of fiber characterization, we input the SFWM-peak experimental data into a genetic algorithm which successfully predicts the values of the parameters that characterize the fiber cross section, as well as predict the particular SFWM process associated with a given pair of peaks. We believe our work will help advance the exploitation of photon-pair correlations in the frequency and polarization degrees of freedom.

Deterministic Distribution of Multipartite Entanglement and Steering in a Quantum Network by Separable States

As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.

Type-Independent Characterization of Spacelike Separated Resources

Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of spacelike separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present Letter, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.

Bipartite Postquantum Steering in Generalized Scenarios

The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the "instrumental steering" scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.

Experimental Demonstration of Robust Quantum Steering

We analyze and experimentally demonstrate quantum steering using criteria based on generalized entropies and criteria with minimal assumptions based on the so-called dimension-bounded steering. Further, we investigate and compare their robustness against experimental imperfections such as misalignment in the shared measurement reference frame. While entropy based criteria are robust against imperfections in state preparation, we demonstrate an advantage in dimension-bounded steering in the presence of measurement imprecision. As steering with such minimal assumptions is easier to reach than fully nonlocal correlations, and as our setting requires very little trust in the measurement devices, the results provide a candidate for the costly Bell tests while remaining highly device independent.

Genuine tripartite Einstein-Podolsky-Rosen steering in the cascaded nonlinear processes of third-harmonic generation

Recently, Einstein-Podolski-Rosen (EPR) steering has important application in quantum information processing, and it has been received considerable attention because of its uniqueness. The properties of quantum steering among three output fields generated by cascaded nonlinear processes of quasi-phase-matching third-harmonic generation in an optical cavity are investigated. Based on the criteria for multipartite EPR steering which proposed by He and Reid [PRL, 111, 250403 (2013)], the genuine tripartite EPR steering among pump, second-harmonic, and third-harmonic is demonstrated. The parameters which affect the quantum property are also discussed.

Tripartite Einstein-Podolsky-Rosen steering with linear and nonlinear beamsplitters in four-wave mixing of Rubidium atoms

Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.

Experimental violation of Mermin steering inequality by three-photon entangled states with nontrivial GHZ-fidelity

Einstein-Podolsky-Rosen steering is an intermediate relationship between entanglement and Bell nonlocality in the hierarchical structure of quantum nonlocality. To certify the steerability of the entangled state, Mermin steering inequality is supposed to be violated by exceeding the inequality bound of 2. We present an experimental generation of post-selected three-photon entangled states and witness a maximal violation of the inequality up to 3.50±0.05. In the context of observing the maximal violation of Mermin steering inequality which requires measuring on the GHZ state, we derive a tight lower bound on the GHZ-fidelity that can be certified from the Mermin steering inequality violation. From this bound, it follows that the violation of Mermin steering inequality by 3.5 certifies the GHZ-fidelity of 78.66% at least. On the other hand, the above maximal violation of Mermin steering inequality observed in our experimental setup is produced by a post-selected entangled state having the GHZ-fidelity of 87.25 ± 0.34% through quantum tomography.

Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light

Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings.

Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

Quantum Steering Beyond Instrumental Causal Networks

We theoretically predict, and experimentally verify with entangled photons, that outcome communication is not enough for hidden-state models to reproduce quantum steering. Hidden-state models with outcome communication correspond, in turn, to the well-known instrumental processes of causal inference but in the one-sided device-independent scenario of one black-box measurement device and one well-characterized quantum apparatus. We introduce one-sided device-independent instrumental inequalities to test against these models, with the appealing feature of detecting entanglement even when communication of the black box's measurement outcome is allowed. We find that, remarkably, these inequalities can also be violated solely with steering, i.e., without outcome communication. In fact, an efficiently computable formal quantifier-the robustness of noninstrumentality-naturally arises, and we prove that steering alone is enough to maximize it. Our findings imply that quantum theory admits a stronger form of steering than known until now, with fundamental as well as practical potential implications.

Spatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks

We introduce the concept of spatio-temporal steering (STS), which reduces, in special cases, to Einstein-Podolsky-Rosen steering and the recently-introduced temporal steering. We describe two measures of this effect referred to as the STS weight and robustness. We suggest that these STS measures enable a new way to assess nonclassical correlations in an open quantum network, such as quantum transport through nano-structures or excitation transfer in a complex biological system. As one of our examples, we apply STS to check nonclassical correlations among sites in a photosynthetic pigment-protein complex in the Fenna-Matthews-Olson model.

Quantum steering: a review with focus on semidefinite programming

Quantum steering refers to the non-classical correlations that can be observed between the outcomes of measurements applied on half of an entangled state and the resulting post-measured states that are left with the other party. From an operational point of view, a steering test can be seen as an entanglement test where one of the parties performs uncharacterised measurements. Thus, quantum steering is a form of quantum inseparability that lies in between the well-known notions of Bell nonlocality and entanglement. Moreover, quantum steering is also related to several asymmetric quantum information protocols where some of the parties are considered untrusted. Because of these facts, quantum steering has received a lot of attention both theoretically and experimentally. The main goal of this review is to give an overview of how to characterise quantum steering through semidefinite programming. This characterisation provides efficient numerical methods to address a number of problems, including steering detection, quantification, and applications. We also give a brief overview of some important results that are not directly related to semidefinite programming. Finally, we make available a collection of semidefinite programming codes that can be used to study the topics discussed in this article.

Quantum Steering Inequality with Tolerance for Measurement-Setting Errors: Experimentally Feasible Signature of Unbounded Violation

Quantum steering is a relatively simple test for proving that the values of quantum-mechanical measurement outcomes come into being only in the act of measurement. By exploiting quantum correlations, Alice can influence-steer-Bob's physical system in a way that is impossible in classical mechanics, as shown by the violation of steering inequalities. Demonstrating this and similar quantum effects for systems of increasing size, approaching even the classical limit, is a long-standing challenging problem. Here, we prove an experimentally feasible unbounded violation of a steering inequality. We derive its universal form where tolerance for measurement-setting errors is explicitly built in by means of the Deutsch-Maassen-Uffink entropic uncertainty relation. Then, generalizing the mutual unbiasedness, we apply the inequality to the multisinglet and multiparticle bipartite Bell state. However, the method is general and opens the possibility of employing multiparticle bipartite steering for randomness certification and development of quantum technologies, e.g., random access codes.

Experimental verification of multipartite entanglement in quantum networks

Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks, it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including the use of system imperfections to their advantage. We demonstrate the verification protocol in a three- and four-party setting using polarization-entangled photons, highlighting its potential for realistic photonic quantum communication and networking applications.

Multipartite entangled states are a fundamental resource for quantum information processing tasks; it is thus important to verify their presence. Here the authors present and demonstrate a protocol that allows any party in a network to verify if an untrusted source is distributing multipartite entangled states.

Extended non-local games and monogamy-of-entanglement games

We study a generalization of non-local games-which we call extended non-local games-in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend on the outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to randomly selected questions. Our study of this class of games was inspired by the monogamy-of-entanglement games introduced by Tomamichel, Fehr, Kaniewski and Wehner, which they also generalize. We prove that a natural extension of the Navascués-Pironio-Acín hierarchy of semidefinite programmes converges to the optimal commuting measurement value of extended non-local games, and we prove two extensions of results of Tomamichel et al. concerning monogamy-of-entanglement games.

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.

Genuinely Multipartite Entangled Quantum States with Fully Local Hidden Variable Models and Hidden Multipartite Nonlocality

The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.

EPR Steering inequalities with Communication Assistance

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information (c = 1), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.

Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems

Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations exhibited by quantum systems that allows for entanglement certification when one of the subsystems is not characterized. Detecting the steerability of quantum states is essential to assess their suitability for quantum information protocols with partially trusted devices. We provide a hierarchy of sufficient conditions for the steerability of bipartite quantum states of any dimension, including continuous variable states. Previously known steering criteria are recovered as special cases of our approach. The proposed method allows us to derive optimal steering witnesses for arbitrary families of quantum states and provides a systematic framework to analytically derive nonlinear steering criteria. We discuss relevant examples and, in particular, provide an optimal steering witness for a lossy single-photon Bell state; the witness can be implemented just by linear optics and homodyne detection and detects steering with a higher loss tolerance than any other known method. Our approach is readily applicable to multipartite steering detection and to the characterization of joint measurability.

Detection of genuine tripartite entanglement and steering in hybrid optomechanics

Multipartite quantum entanglement is a key resource for ensuring security in quantum network. We show that by using a unified parameter in terms of reduced noise variances one can determine different types of tripartite entanglement of a given state generated in a hybrid optomechanical system, where an atomic ensemble is located inside a single-mode cavity with a movable mirror, with different thresholds for each type. In particular, the special quantum states which allow both entanglement and steering genuinely shared among atom-light-mirror modes can be observed, even though there is no direct interaction between the mirror and the atomic ensemble. We further show the robustness against mechanical thermal noise and damping, the relaxation time of atomic ensemble, as well as the effect of gain factors involved in the criteria. Our analysis provides an experimentally achievable method to determine the type of tripartite quantum correlation in a way.

Postquantum Steering

The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While post-quantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.