1
|
Arvidsson-Shukur DRM, McConnell AG, Yunger Halpern N. Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves. PHYSICAL REVIEW LETTERS 2023; 131:150202. [PMID: 37897785 DOI: 10.1103/physrevlett.131.150202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2022] [Revised: 09/08/2023] [Accepted: 09/11/2023] [Indexed: 10/30/2023]
Abstract
We construct a metrology experiment in which the metrologist can sometimes amend the input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change the input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist's winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.
Collapse
Affiliation(s)
| | - Aidan G McConnell
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom
- Laboratory for X-ray Nanoscience and Technologies, Paul Scherrer Institut, 5232 Villigen, Switzerland
- Department of Physics and Quantum Center, Eidgenössische Technische Hochschule Zürich, CH-8093 Zürich, Switzerland
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
2
|
Okamoto R, Cohen E. Experimentally probing anomalous time evolution of a single photon. PNAS NEXUS 2023; 2:pgad157. [PMID: 37265544 PMCID: PMC10230160 DOI: 10.1093/pnasnexus/pgad157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 04/26/2023] [Accepted: 05/01/2023] [Indexed: 06/03/2023]
Abstract
In quantum mechanics, a quantum system is irreversibly collapsed by a projective measurement. Hence, delicately probing the time evolution of a quantum system holds the key to understanding curious phenomena. Here, we experimentally explore an anomalous time evolution, where, illustratively, a particle disappears from a box and emerges in a different box, with a certain moment in which it can be found in neither of them. In this experiment, we directly probe this curious time evolution of a single photon by measuring up to triple-operator sequential weak values (SWVs) using a novel probeless scheme. The naive interpretation provided by single-operator weak values (WVs) seems to imply the "disappearance" and "re-appearance" of a photon as theoretically predicted. However, double- and triple-operator SWVs, representing temporal correlations between the aforementioned values, show that spatial information about the photon does not entirely vanish in the intermediate time. These results show that local values (in space and time) alone, such as single-operator WVs, cannot fully explain all types of quantum evolution in time-higher order correlations are necessary in general, shedding new light on time evolution in quantum mechanics. The probeless measurement technique proposed here for measuring multiple-operator WVs can be straightforwardly extended to study various other cases of curious quantum evolution in time.
Collapse
|
3
|
Lupu-Gladstein N, Yilmaz YB, Arvidsson-Shukur DRM, Brodutch A, Pang AOT, Steinberg AM, Halpern NY. Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment. PHYSICAL REVIEW LETTERS 2022; 128:220504. [PMID: 35714243 DOI: 10.1103/physrevlett.128.220504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities-quantum extensions of probabilities-engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate's birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter's amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA's metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.
Collapse
Affiliation(s)
- Noah Lupu-Gladstein
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Y Batuhan Yilmaz
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | | | - Aharon Brodutch
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Arthur O T Pang
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Aephraim M Steinberg
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
4
|
Kim Y, Yoo SY, Kim YH. Heisenberg-Limited Metrology via Weak-Value Amplification without Using Entangled Resources. PHYSICAL REVIEW LETTERS 2022; 128:040503. [PMID: 35148150 DOI: 10.1103/physrevlett.128.040503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.
Collapse
Affiliation(s)
- Yosep Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Seung-Yeun Yoo
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Yoon-Ho Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| |
Collapse
|
5
|
Song M, Steinmetz J, Zhang Y, Nauriyal J, Lyons K, Jordan AN, Cardenas J. Enhanced on-chip phase measurement by inverse weak value amplification. Nat Commun 2021; 12:6247. [PMID: 34716353 PMCID: PMC8556267 DOI: 10.1038/s41467-021-26522-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 10/05/2021] [Indexed: 12/01/2022] Open
Abstract
Optical interferometry plays an essential role in precision metrology such as in gravitational wave detection, gyroscopes, and environmental sensing. Weak value amplification enables reaching the shot-noise-limit of sensitivity, which is difficult for most optical sensors, by amplifying the interferometric signal without amplifying certain technical noises. We implement a generalized form of weak value amplification on an integrated photonic platform with a multi-mode interferometer. Our results pave the way for a more sensitive, robust, and compact platform for measuring phase, which can be adapted to fields such as coherent communications and the quantum domain. In this work, we show a 7 dB signal enhancement in our weak value device over a standard Mach-Zehnder interferometer with equal detected optical power, as well as frequency measurements with 2 kHz sensitivity by adding a ring resonator.
Collapse
Affiliation(s)
- Meiting Song
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
| | - John Steinmetz
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
| | - Yi Zhang
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
| | - Juniyali Nauriyal
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA
- Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY, 14627, USA
| | - Kevin Lyons
- Hoplite AI, 2 Fox Glen Ct., Clifton Park, NY, 12065, USA
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
- Institute for Quantum Studies, Chapman University, Orange, CA, 92866, USA
| | - Jaime Cardenas
- The Institute of Optics, University of Rochester, Rochester, NY, 14627, USA.
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA.
| |
Collapse
|
6
|
Rebufello E, Piacentini F, Avella A, Souza MAD, Gramegna M, Dziewior J, Cohen E, Vaidman L, Degiovanni IP, Genovese M. Anomalous weak values via a single photon detection. LIGHT, SCIENCE & APPLICATIONS 2021; 10:106. [PMID: 34035219 PMCID: PMC8149841 DOI: 10.1038/s41377-021-00539-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Revised: 04/07/2021] [Accepted: 04/19/2021] [Indexed: 06/12/2023]
Abstract
Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result1. This theoretical prediction, called weak value, was realised in numerous experiments2-9, but its meaning remains very controversial10-19, since its "anomalous" nature, i.e., the possibility to exceed the eigenvalue spectrum, as well as its "quantumness" are debated20-22. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without the need for statistical averaging. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, demonstrating their non-statistical, single-particle nature, this result represents a breakthrough in understanding the foundations of quantum measurement, showing unprecedented measurement capability for further applications of weak values to quantum photonics.
Collapse
Affiliation(s)
| | | | | | - Muriel A de Souza
- National Institute of Metrology, Quality and Technology-INMETRO, Av. Nossa Senhora das Graças, 50, Duque de Caxias, RJ, 25250-020, Brazil
| | | | - Jan Dziewior
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748, Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, 80797, München, Germany
| | - Eliahu Cohen
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, 5290002, Israel
| | - Lev Vaidman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, 6997801, Israel
| | | | | |
Collapse
|
7
|
Monroe JT, Yunger Halpern N, Lee T, Murch KW. Weak Measurement of a Superconducting Qubit Reconciles Incompatible Operators. PHYSICAL REVIEW LETTERS 2021; 126:100403. [PMID: 33784149 DOI: 10.1103/physrevlett.126.100403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 11/19/2020] [Accepted: 01/29/2021] [Indexed: 06/12/2023]
Abstract
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements' incompatibility, via backaction on the state. Mathematically, a weak value-a preselected and postselected expectation value-lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement's ability to reconcile incompatible operations.
Collapse
Affiliation(s)
- Jonathan T Monroe
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Nicole Yunger Halpern
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Taeho Lee
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| |
Collapse
|
8
|
Stárek R, Mičuda M, Hošák R, Ježek M, Fiurášek J. Experimental entanglement-assisted weak measurement of phase shift. OPTICS EXPRESS 2020; 28:34639-34655. [PMID: 33182927 DOI: 10.1364/oe.403711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 10/14/2020] [Indexed: 06/11/2023]
Abstract
Weak value amplification is a popular method in quantum metrology for enhancing the sensitivity at the expense of the signal intensity. Recently, it was suggested that the trade-off between signal intensity and sensitivity can be improved by using an entangled auxiliary system. Here, we experimentally investigate such entanglement-assisted weak measurement of small conditional phase shifts induced by an interaction between ancilla and meter qubits. We utilize entangled photon pairs and implement the required three-qubit quantum logic circuit with linear optics. The circuit comprises a two-qubit controlled phase gate and a three-qubit controlled-controlled phase gate with fully tunable conditional phase shifts. We fully characterize the output states of our circuit by quantum state tomography and perform a comprehensive analysis of the trade-off between the measurement sensitivity and the success probability of the protocol. The observed experimental results are in good qualitative agreement with theoretical predictions, but the overall performance of our setup is limited by various experimental imperfections. We provide a detailed theoretical analysis of the influence of dephasing of the entangled ancilla state, which is one of the main sources of imperfections in the experiment. We also discuss the ultimate scaling with the dimension of the entangled ancilla system.
Collapse
|
9
|
Arvidsson-Shukur DRM, Yunger Halpern N, Lepage HV, Lasek AA, Barnes CHW, Lloyd S. Quantum advantage in postselected metrology. Nat Commun 2020; 11:3775. [PMID: 32728082 PMCID: PMC7391714 DOI: 10.1038/s41467-020-17559-w] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 07/08/2020] [Indexed: 11/08/2022] Open
Abstract
In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.
Collapse
Affiliation(s)
- David R M Arvidsson-Shukur
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK.
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Nicole Yunger Halpern
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Hugo V Lepage
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Aleksander A Lasek
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Crispin H W Barnes
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Seth Lloyd
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| |
Collapse
|
10
|
Chen G, Zhang L, Zhang WH, Peng XX, Xu L, Liu ZD, Xu XY, Tang JS, Sun YN, He DY, Xu JS, Zhou ZQ, Li CF, Guo GC. Achieving Heisenberg-Scaling Precision with Projective Measurement on Single Photons. PHYSICAL REVIEW LETTERS 2018; 121:060506. [PMID: 30141679 DOI: 10.1103/physrevlett.121.060506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2018] [Indexed: 06/08/2023]
Abstract
It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^{6} in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurements, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ∼n^{2} and leads to a practical precision ≃1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.
Collapse
Affiliation(s)
- Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Liang Xu
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Zhao-Di Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Shun Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yong-Nan Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - De-Yong He
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zong-Quan Zhou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| |
Collapse
|
11
|
Chen G, Aharon N, Sun YN, Zhang ZH, Zhang WH, He DY, Tang JS, Xu XY, Kedem Y, Li CF, Guo GC. Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states. Nat Commun 2018; 9:93. [PMID: 29311543 PMCID: PMC5758646 DOI: 10.1038/s41467-017-02487-z] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Accepted: 12/03/2017] [Indexed: 11/09/2022] Open
Abstract
Improving the precision of measurements is a significant scientific challenge. Previous works suggest that in a photon-coupling scenario the quantum fisher information shows a quantum-enhanced scaling of N2, which in theory allows a better-than-classical scaling in practical measurements. In this work, utilizing mixed states with a large uncertainty and a post-selection of an additional pure system, we present a scheme to extract this amount of quantum fisher information and experimentally attain a practical Heisenberg scaling. We performed a measurement of a single-photon's Kerr non-linearity with a Heisenberg scaling, where an ultra-small Kerr phase of ≃6 × 10-8 rad was observed with a precision of ≃3.6 × 10-10 rad. From the use of mixed states, the upper bound of quantum fisher information is improved to 2N2. Moreover, by using an imaginary weak-value the scheme is robust to noise originating from the self-phase modulation.
Collapse
Affiliation(s)
- Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Nati Aharon
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 91904,, Givat Ram, Israel
| | - Yong-Nan Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Zi-Huai Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - De-Yong He
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Jian-Shun Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Yaron Kedem
- Department of Physics, AlbaNova University Center, Stockholm University, 106 91, Stockholm, Sweden.
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China. .,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| |
Collapse
|
12
|
Liu WT, Martínez-Rincón J, Viza GI, Howell JC. Anomalous amplification of a homodyne signal via almost-balanced weak values. OPTICS LETTERS 2017; 42:903-906. [PMID: 28248327 DOI: 10.1364/ol.42.000903] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We propose precision measurements of ultra-small angular velocities of a mirror within a modified Sagnac interferometer, where the counter-propagating beams are spatially separated, using the recently proposed technique of almost-balanced weak values amplification (ABWV) [Phys. Rev. Lett.116, 100803 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.100803]. The separation between the two beams provides additional amplification with respect to using collinear beams in a Sagnac interferometer. Within the same setup, the weak-value amplification technique is also performed for comparison. Much higher amplification factors can be obtained using the almost-balanced weak values technique, with the best one achieved in our experiments being as high as 1.2×107. In addition, the amplification factor monotonically increases with decreasing of the post-selection phase for the ABWV case in our experiments, which is not the case for weak-value amplification (WVA) at small post-selection phases. Both techniques consist of measuring the angular velocity. The sensitivity of the ABWV technique is ∼38 nrad/s per averaged pulse for a repetition rate of 1 Hz and ∼33 nrad/s per averaged pulse for the WVA technique.
Collapse
|
13
|
Harris J, Boyd RW, Lundeen JS. Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation. PHYSICAL REVIEW LETTERS 2017; 118:070802. [PMID: 28256865 DOI: 10.1103/physrevlett.118.070802] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Indexed: 06/06/2023]
Abstract
Weak value amplification (WVA) is a technique by which one can magnify the apparent strength of a measurement signal. Some have claimed that WVA can outperform more conventional measurement schemes in parameter estimation. Nonetheless, a significant body of theoretical work has challenged this perspective, suggesting WVA to be fundamentally suboptimal. Optimal measurements may not be practical, however. Two practical considerations that have been conjectured to afford a benefit to WVA over conventional measurement are certain types of noise and detector saturation. Here, we report a theoretical study of the role of saturation and pixel noise in WVA-based measurement, in which we carry out a Bayesian analysis of the Fisher information available using a saturable, pixelated, digitized, and/or noisy detector. We draw two conclusions: first, that saturation alone does not confer an advantage to the WVA approach over conventional measurement, and second, that WVA can outperform conventional measurement when saturation is combined with intrinsic pixel noise and/or digitization.
Collapse
Affiliation(s)
- Jérémie Harris
- Max Planck Centre for Extreme and Quantum Photonics, Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Robert W Boyd
- Max Planck Centre for Extreme and Quantum Photonics, Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
- Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Jeff S Lundeen
- Max Planck Centre for Extreme and Quantum Photonics, Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| |
Collapse
|
14
|
Wang YT, Tang JS, Hu G, Wang J, Yu S, Zhou ZQ, Cheng ZD, Xu JS, Fang SZ, Wu QL, Li CF, Guo GC. Experimental Demonstration of Higher Precision Weak-Value-Based Metrology Using Power Recycling. PHYSICAL REVIEW LETTERS 2016; 117:230801. [PMID: 27982616 DOI: 10.1103/physrevlett.117.230801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2016] [Indexed: 06/06/2023]
Abstract
The weak-value-based metrology is very promising and has attracted a lot of attention in recent years because of its remarkable ability in signal amplification. However, it is suggested that the upper limit of the precision of this metrology cannot exceed that of classical metrology because of the low sample size caused by the probe loss during postselection. Nevertheless, a recent proposal shows that this probe loss can be reduced by the power-recycling technique, and thus enhance the precision of weak-value-based metrology. Here we experimentally realize the power-recycled interferometric weak-value-based beam-deflection measurement and obtain the amplitude of the detected signal and white noise by discrete Fourier transform. Our results show that the detected signal can be strengthened by power recycling, and the power-recycled weak-value-based signal-to-noise ratio can surpass the upper limit of the classical scheme, corresponding to the shot-noise limit. This work sheds light on higher precision metrology and explores the real advantage of the weak-value-based metrology over classical metrology.
Collapse
Affiliation(s)
- Yi-Tao Wang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jian-Shun Tang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Gang Hu
- Department of Physics, Central China Normal University, Wuhan 430079, People's Republic of China
| | - Jian Wang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Shang Yu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zong-Quan Zhou
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Ze-Di Cheng
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jin-Shi Xu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Sen-Zhi Fang
- Department of Physics, Central China Normal University, Wuhan 430079, People's Republic of China
| | - Qing-Lin Wu
- Department of Physics, Central China Normal University, Wuhan 430079, People's Republic of China
| | - Chuan-Feng Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| |
Collapse
|
15
|
Pang S, Brun TA. Improving the Precision of Weak Measurements by Postselection Measurement. PHYSICAL REVIEW LETTERS 2015; 115:120401. [PMID: 26430972 DOI: 10.1103/physrevlett.115.120401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2014] [Indexed: 06/05/2023]
Abstract
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.
Collapse
Affiliation(s)
- Shengshi Pang
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Todd A Brun
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
| |
Collapse
|
16
|
Lyons K, Dressel J, Jordan AN, Howell JC, Kwiat PG. Power-recycled weak-value-based metrology. PHYSICAL REVIEW LETTERS 2015; 114:170801. [PMID: 25978218 DOI: 10.1103/physrevlett.114.170801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2015] [Indexed: 06/04/2023]
Abstract
We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in all the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.
Collapse
Affiliation(s)
- Kevin Lyons
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
| | - Justin Dressel
- Department of Electrical and Computer Engineering; University of California, Riverside, California 92521, USA
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, California 92866, USA
| | - John C Howell
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
| | - Paul G Kwiat
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA
| |
Collapse
|