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Grygar J, Hloušek J, Fiurášek J, Ježek M. Quantum non-Gaussianity certification of photon number-resolving detectors. OPTICS EXPRESS 2022; 30:33097-33111. [PMID: 36242357 DOI: 10.1364/oe.463786] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 08/03/2022] [Indexed: 06/16/2023]
Abstract
We report on direct experimental certification of the quantum non-Gaussian character of a photon number-resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements Π^m associated with the m-fold coincidence counts, up to m = 7. The experimental ability to certify from the first principles the quantum non-Gaussian character of Π^m is for large m limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.
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Fiurášek J. Efficient construction of witnesses of the stellar rank of nonclassical states of light. OPTICS EXPRESS 2022; 30:30630-30639. [PMID: 36242163 DOI: 10.1364/oe.466175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 07/22/2022] [Indexed: 06/16/2023]
Abstract
The stellar hierarchy of quantum states of light classifies the states according to the Fock-state resources that are required for their generation together with unitary Gaussian operations. States with stellar rank n can be also equivalently referred to as genuinely n-photon quantum non-Gaussian states. Here we present an efficient method for construction of general witnesses of the stellar rank. The number of parameters that need to be optimized in order to determine the witness does not depend on the stellar rank and it scales quadratically with the number of modes. We illustrate the procedure by constructing stellar rank witnesses based on pairs of Fock state probabilities and also based on pairs of fidelities with superpositions of coherent states.
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de Gosson MA. Symplectic Radon Transform and the Metaplectic Representation. ENTROPY (BASEL, SWITZERLAND) 2022; 24:761. [PMID: 35741482 PMCID: PMC9222323 DOI: 10.3390/e24060761] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 05/13/2022] [Accepted: 05/14/2022] [Indexed: 11/17/2022]
Abstract
We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional quantum systems. We interpret the Radon transform of a quantum state as a generalized marginal distribution for its Wigner transform; the inverse Radon transform thus appears as a "demarginalization process" for the Wigner distribution.
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Affiliation(s)
- Maurice A de Gosson
- Faculty of Mathematics (NuHAG), University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
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Estimating Non-Gaussianity of a Quantum State by Measuring Orthogonal Quadratures. ENTROPY 2022; 24:e24020289. [PMID: 35205583 PMCID: PMC8871266 DOI: 10.3390/e24020289] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 02/10/2022] [Accepted: 02/17/2022] [Indexed: 02/04/2023]
Abstract
We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.
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Hloušek J, Ježek M, Fiurášek J. Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors. PHYSICAL REVIEW LETTERS 2021; 126:043601. [PMID: 33576686 DOI: 10.1103/physrevlett.126.043601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2020] [Accepted: 01/06/2021] [Indexed: 06/12/2023]
Abstract
Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.
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Affiliation(s)
- Josef Hloušek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
| | - Miroslav Ježek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
| | - Jaromír Fiurášek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 77146 Olomouc, Czech Republic
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Sperling J, Phillips DS, Bulmer JFF, Thekkadath GS, Eckstein A, Wolterink TAW, Lugani J, Nam SW, Lita A, Gerrits T, Vogel W, Agarwal GS, Silberhorn C, Walmsley IA. Detector-Agnostic Phase-Space Distributions. PHYSICAL REVIEW LETTERS 2020; 124:013605. [PMID: 31976720 DOI: 10.1103/physrevlett.124.013605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Indexed: 06/10/2023]
Abstract
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.
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Affiliation(s)
- J Sperling
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - D S Phillips
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J F F Bulmer
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - G S Thekkadath
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - A Eckstein
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - T A W Wolterink
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J Lugani
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S W Nam
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - A Lita
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T Gerrits
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - W Vogel
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23, D-18059 Rostock, Germany
| | - G S Agarwal
- Texas A&M University, College Station, Texas 77845, USA
| | - C Silberhorn
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - I A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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Entropic nonclassicality and quantum non-Gaussianity tests via beam splitting. Sci Rep 2019; 9:17835. [PMID: 31780692 PMCID: PMC6882878 DOI: 10.1038/s41598-019-54110-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Accepted: 11/08/2019] [Indexed: 11/21/2022] Open
Abstract
We propose entropic nonclassicality criteria for quantum states of light that can be readily tested using homodyne detection with beam splitting operation. Our method draws on the fact that the entropy of quadrature distributions for a classical state is non-increasing under an arbitrary loss channel. We show that our test is strictly stronger than the variance-based squeezing condition and that it can also be extended to detect quantum non-Gaussianity in conjunction with phase randomization. Furthermore, we address how our criteria can be used to identify single-mode resource states to generate two-mode states demonstrating EPR paradox, i.e., quantum steering, via beam-splitter setting.
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Hloušek J, Dudka M, Straka I, Ježek M. Accurate Detection of Arbitrary Photon Statistics. PHYSICAL REVIEW LETTERS 2019; 123:153604. [PMID: 31702281 DOI: 10.1103/physrevlett.123.153604] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2018] [Indexed: 06/10/2023]
Abstract
We report a measurement workflow free of systematic errors consisting of a reconfigurable photon-number-resolving detector, custom electronic circuitry, and faithful data-processing algorithm. We achieve an unprecedented accurate measurement of various photon-number distributions going beyond the number of detection channels with an average fidelity of 0.998, where the error is primarily caused by the sources themselves. Mean numbers of photons cover values up to 20 and faithful autocorrelation measurements range from g^{(2)}=6×10^{-3} to 2. We successfully detect chaotic, classical, nonclassical, non-Gaussian, and negative-Wigner-function light. Our results open new paths for optical technologies by providing full access to the photon-number information without the necessity of detector tomography.
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Affiliation(s)
- Josef Hloušek
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czechia
| | - Michal Dudka
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czechia
| | - Ivo Straka
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czechia
| | - Miroslav Ježek
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czechia
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Bohmann M, Tiedau J, Bartley T, Sperling J, Silberhorn C, Vogel W. Incomplete Detection of Nonclassical Phase-Space Distributions. PHYSICAL REVIEW LETTERS 2018; 120:063607. [PMID: 29481264 DOI: 10.1103/physrevlett.120.063607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 06/08/2023]
Abstract
We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
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Affiliation(s)
- M Bohmann
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - J Tiedau
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - T Bartley
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - J Sperling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - C Silberhorn
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - W Vogel
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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