1
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Jing F, Liu W, Kong L, He C. Improving the Performance of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution via a Noiseless Linear Amplifier. ENTROPY 2021; 23:e23121691. [PMID: 34945997 PMCID: PMC8700696 DOI: 10.3390/e23121691] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 12/11/2021] [Accepted: 12/14/2021] [Indexed: 11/16/2022]
Abstract
In the continuous variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol, both Alice and Bob send quantum states to an untrusted third party, Charlie, for detection through the quantum channel. In this paper, we mainly study the performance of the CV-MDI-QKD system using the noiseless linear amplifier (NLA). The NLA is added to the output of the detector at Charlie’s side. The research results show that NLA can increase the communication distance and secret key rate of the CV-MDI-QKD protocol. Moreover, we find that the more powerful the improvement of the performance with the longer gain of NLA and the optimum gain is given under different conditions.
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Affiliation(s)
| | | | | | - Chen He
- Correspondence: (W.L.); (C.H.)
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2
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Biagi N, Bohmann M, Agudelo E, Bellini M, Zavatta A. Experimental Certification of Nonclassicality via Phase-Space Inequalities. PHYSICAL REVIEW LETTERS 2021; 126:023605. [PMID: 33512213 DOI: 10.1103/physrevlett.126.023605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi Q functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.
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Affiliation(s)
- Nicola Biagi
- Istituto Nazionale di Ottica (CNR-INO), L.go E. Fermi 6, 50125 Florence, Italy
- LENS and Department of Physics & Astronomy, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy
| | - Martin Bohmann
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science and Technology (VCQ), Vienna, Austria
| | - Elizabeth Agudelo
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Marco Bellini
- Istituto Nazionale di Ottica (CNR-INO), L.go E. Fermi 6, 50125 Florence, Italy
- LENS and Department of Physics & Astronomy, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy
| | - Alessandro Zavatta
- Istituto Nazionale di Ottica (CNR-INO), L.go E. Fermi 6, 50125 Florence, Italy
- LENS and Department of Physics & Astronomy, University of Firenze, 50019 Sesto Fiorentino, Florence, Italy
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3
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Peng ZA, Zhao T, Yang GQ, Huang GM, Li GX. Multifold wave-particle quantum correlations in strongly correlated three-photon emissions from filtered resonance fluorescence. OPTICS EXPRESS 2020; 28:22767-22790. [PMID: 32752533 DOI: 10.1364/oe.396684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 06/28/2020] [Indexed: 06/11/2023]
Abstract
Multifold wave-particle quantum correlations are studied in strongly correlated three-photon emissions from the Mollow triplet via frequency engineering. The nonclassicality and the non-Gaussianity of the filtered field are discussed by correlating intensity signal and correlated balanced homodyne signals. Due to the non-Gaussian fluctuations in the Mollow triplet, new forms of the criterion of nonclassicality for non-Gaussian radiation are proposed by introducing intensity-dual quadrature correlation functions, which contain the information about strongly correlated three-photon emissions of the Mollow triplet. In addition, the time-dependent dynamics of non-Gaussian fluctuations of the filtered field is studied, which displays conspicuous asymmetry. Physically, the asymmetrical evolution of non-Gaussian fluctuations can be attributed to the different transition dynamics of the laser-dressed quantum emitter revealed by the past quantum state and conditional quantum state. Compared with the conventional three-photon intensity correlations that unilaterally reflect the particle properties of radiation, the multifold wave-particle correlation functions we proposed may convey more information about wave-particle duality of radiation, such as the quantum coherence of photon triplet and "which-path" in cascaded photon emissions in atomic systems.
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4
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Bohmann M, Agudelo E. Phase-Space Inequalities Beyond Negativities. PHYSICAL REVIEW LETTERS 2020; 124:133601. [PMID: 32302197 DOI: 10.1103/physrevlett.124.133601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.
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Affiliation(s)
- Martin Bohmann
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Elizabeth Agudelo
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
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5
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Nehra R, Chang CH, Yu Q, Beling A, Pfister O. Photon-number-resolving segmented detectors based on single-photon avalanche-photodiodes. OPTICS EXPRESS 2020; 28:3660-3675. [PMID: 32122030 DOI: 10.1364/oe.380416] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Accepted: 01/16/2020] [Indexed: 06/10/2023]
Abstract
We investigate the feasibility and performance of photon-number-resolved photodetection employing single-photon avalanche photodiodes (SPADs) with low dark counts. While the main idea, to split n photons into m detection modes with a vanishing probability of more than one photon per mode, is not new, we investigate here a important variant of this situation where SPADs are side-coupled to the same waveguide rather than terminally coupled to a propagation tree. This prevents the nonideal SPAD quantum efficiency from contributing to photon loss. We propose a concrete SPAD segmented waveguide detector based on a vertical directional coupler design, and characterize its performance by evaluating the purities of Positive-Operator-Valued Measures (POVMs) in terms of number of SPADs, photon loss, dark counts, and electrical cross-talk.
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6
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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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7
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Abstract
We show, in a formal way, how a class of complex quasiprobability distribution functions may be introduced by using the fractional Fourier transform. This leads to the Fresnel transform of a characteristic function instead of the usual Fourier transform. We end the manuscript by showing a way in which the distribution we are introducing may be reconstructed by using atom-field interactions.
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8
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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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9
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Bina M, Allevi A, Bondani M, Olivares S. Homodyne-like detection for coherent state-discrimination in the presence of phase noise. OPTICS EXPRESS 2017; 25:10685-10692. [PMID: 28468439 DOI: 10.1364/oe.25.010685] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose a homodyne-like detection scheme involving photon-number-resolving detectors to discriminate between two coherent states affected by either uniform or gaussian phase noise. A proof-of-principle experiment is performed employing two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number differences. The performance of the strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a function of the characteristic noise parameters.
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10
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Kühn B, Vogel W. Unbalanced Homodyne Correlation Measurements. PHYSICAL REVIEW LETTERS 2016; 116:163603. [PMID: 27152803 DOI: 10.1103/physrevlett.116.163603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Indexed: 06/05/2023]
Abstract
A method is introduced that allows one to measure normal-ordered moments of the displaced photon-number operator up to higher orders, without the need of photon-number resolving detectors. It is based on unbalanced homodyne correlation measurements, with the local oscillator being replaced by a displaced dephased laser. The measured moments yield a simple approximation of quasiprobabilities, representing the full quantum state. Quantum properties of light are efficiently certified through normal-ordered observables directly accessible by our method, which is illustrated for a weakly squeezed vacuum and a single-photon-added thermal state.
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Affiliation(s)
- B Kühn
- Arbeitsgruppe Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - W Vogel
- Arbeitsgruppe Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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11
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Harder G, Silberhorn C, Rehacek J, Hradil Z, Motka L, Stoklasa B, Sánchez-Soto LL. Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics. PHYSICAL REVIEW LETTERS 2016; 116:133601. [PMID: 27081977 DOI: 10.1103/physrevlett.116.133601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 06/05/2023]
Abstract
We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy. The method allows us to reliably infer the squeezing of genuine two-mode states without any phase reference.
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Affiliation(s)
- G Harder
- Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
| | - Ch Silberhorn
- Department of Physics, University of Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
- Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany
| | - J Rehacek
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - Z Hradil
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - L Motka
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - B Stoklasa
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - L L Sánchez-Soto
- Max-Planck-Institut für die Physik des Lichts, Günther-Scharowsky-Straße 1, Bau 24, 91058 Erlangen, Germany
- Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
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12
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Hofer SG, Lehnert KW, Hammerer K. Proposal to Test Bell's Inequality in Electromechanics. PHYSICAL REVIEW LETTERS 2016; 116:070406. [PMID: 26943516 DOI: 10.1103/physrevlett.116.070406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2015] [Indexed: 06/05/2023]
Abstract
Optomechanical and electromechanical systems offer an effective platform to test quantum theory and its predictions at macroscopic scales. To date, all experiments presuppose the validity of quantum mechanics, but could in principle be described by a hypothetical local statistical theory. Here we suggest a Bell test using the electromechanical Einstein-Podolski-Rosen entangled state recently generated by Palomaki et al., Science 342, 710 (2013), which would rule out any local and realistic explanation of the measured data without assuming the validity of quantum mechanics at macroscopic scales. It additionally provides a device-independent way to verify electromechanical entanglement. The parameter regime required for our scheme has been demonstrated or is within reach of current experiments.
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Affiliation(s)
- Sebastian G Hofer
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Institute for Theoretical Physics, Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Konrad W Lehnert
- JILA, National Institute of Standards and Technology and the University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Klemens Hammerer
- Institute for Theoretical Physics, Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University Hannover, Callinstraße 38, 30167 Hannover, Germany
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13
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Luis A, Sperling J, Vogel W. Nonclassicality phase-space functions: more insight with fewer detectors. PHYSICAL REVIEW LETTERS 2015; 114:103602. [PMID: 25815932 DOI: 10.1103/physrevlett.114.103602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2014] [Indexed: 06/04/2023]
Abstract
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click-counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, a small number of on-off diodes can yield more insight than perfect photon number resolution. Quantum signatures in the particle and wave domain of the quantized radiation field, as shown by photon number and squeezed states, respectively, will be uncovered in terms of negativities of the sampled phase-space functions. Application in the vast fields of quantum optics and quantum technology will benefit from our efficient nonclassicality characterization approach.
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Affiliation(s)
- Alfredo Luis
- Departamento de Óptica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
| | - Jan Sperling
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Werner Vogel
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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14
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Donati G, Bartley TJ, Jin XM, Vidrighin MD, Datta A, Barbieri M, Walmsley IA. Observing optical coherence across Fock layers with weak-field homodyne detectors. Nat Commun 2014; 5:5584. [PMID: 25427457 DOI: 10.1038/ncomms6584] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2014] [Accepted: 10/17/2014] [Indexed: 11/09/2022] Open
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15
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Lundeen JS, Bamber C. Procedure for direct measurement of general quantum states using weak measurement. PHYSICAL REVIEW LETTERS 2012; 108:070402. [PMID: 22401180 DOI: 10.1103/physrevlett.108.070402] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2011] [Indexed: 05/31/2023]
Abstract
Recent work by Lundeen et al. [Nature (London) 474, 188 (2011)] directly measured the wave function by weakly measuring a variable followed by a normal (i.e., "strong") measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed in situ, determining the quantum state without destroying it.
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Affiliation(s)
- Jeff S Lundeen
- Institute for National Measurement Standards, National Research Council, Ottawa, Ontario, Canada.
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16
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Laiho K, Cassemiro KN, Gross D, Silberhorn C. Probing the negative Wigner function of a pulsed single photon point by point. PHYSICAL REVIEW LETTERS 2010; 105:253603. [PMID: 21231590 DOI: 10.1103/physrevlett.105.253603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2010] [Indexed: 05/30/2023]
Abstract
We investigate quantum properties of pulsed light fields point by point in phase space. We probe the negative region of the Wigner function of a single photon generated by the means of waveguided parametric down conversion. This capability is achieved by employing loss-tolerant photon-number resolving detection, allowing us to directly observe the oscillations of the photon statistics in dependence of applied displacements in phase space. Our scheme is highly mode sensitive and can reveal the single-mode character of the signal state.
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Affiliation(s)
- Kaisa Laiho
- Max Planck Institute for Science of Light, Günther-Scharowsky-straße 1/Building 24, 91058 Erlangen, Germany.
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17
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Bondani M, Allevi A, Andreoni A. Wigner function of pulsed fields by direct detection. OPTICS LETTERS 2009; 34:1444-1446. [PMID: 19412300 DOI: 10.1364/ol.34.001444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We present the reconstruction of the Wigner function of some classical pulsed optical states obtained by direct measurement of the detected-photon probability distributions of the state displaced by a coherent field. We use a photodetector endowed with internal gain, which is operated in the non-photon-resolving regime. The measurements are performed up to mesoscopic intensities (up to more than 30 photons per pulse). The method can be applied to characterize nonclassical continuous-variable states.
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Affiliation(s)
- Maria Bondani
- National Laboratory for Ultrafast and Ultraintense Optical Science-CNR-INFM, Como, I-22100, Italy.
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18
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Puentes G, Lundeen JS, Branderhorst MPA, Coldenstrodt-Ronge HB, Smith BJ, Walmsley IA. Bridging particle and wave sensitivity in a configurable detector of positive operator-valued measures. PHYSICAL REVIEW LETTERS 2009; 102:080404. [PMID: 19257725 DOI: 10.1103/physrevlett.102.080404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2008] [Indexed: 05/27/2023]
Abstract
We report an optical detector with tunable positive operator-valued measures. The device is based on a combination of weak-field homodyne techniques and photon-number-resolving detection. The resulting positive operator-valued measures can be continuously tuned from Fock-state projectors to a variety of phase-dependent quantum-state measurements by adjusting different system parameters such as local oscillator coupling, amplitude, and phase, allowing thus not only detection but also preparation of exotic quantum states. Experimental tomographic reconstructions of classical benchmark states are presented as a demonstration of the detector capabilities.
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Affiliation(s)
- Graciana Puentes
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
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19
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Hradil Z, Mogilevtsev D, Rehácek J. Biased tomography schemes: an objective approach. PHYSICAL REVIEW LETTERS 2006; 96:230401. [PMID: 16803354 DOI: 10.1103/physrevlett.96.230401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2005] [Indexed: 05/10/2023]
Abstract
We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.
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Affiliation(s)
- Z Hradil
- Department of Optics, Palacky University, 17. listopadu 50, 77200 Olomouc, Czech Republic
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20
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Shchukin E, Vogel W. Universal measurement of quantum correlations of radiation. PHYSICAL REVIEW LETTERS 2006; 96:200403. [PMID: 16803157 DOI: 10.1103/physrevlett.96.200403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2006] [Indexed: 05/10/2023]
Abstract
A measurement technique is proposed which, in principle, allows one to observe the general space-time correlation properties of a quantized radiation field. Our method, called balanced homodyne correlation measurement, unifies the advantages of balanced homodyne detection with those of homodyne correlation measurements.
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Affiliation(s)
- E Shchukin
- Arbeitsgruppe Quantenoptik, Fachbereich Physik, Universität Rostock, D-18051 Rostock, Germany.
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21
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Mukamel E, Banaszek K, Walmsley IA, Dorrer C. Direct measurement of the spatial Wigner function with area-integrated detection. OPTICS LETTERS 2003; 28:1317-1319. [PMID: 12906075 DOI: 10.1364/ol.28.001317] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.
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Affiliation(s)
- Eran Mukamel
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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Lougovski P, Solano E, Zhang ZM, Walther H, Mack H, Schleich WP. Fresnel representation of the Wigner function: an operational approach. PHYSICAL REVIEW LETTERS 2003; 91:010401. [PMID: 12906520 DOI: 10.1103/physrevlett.91.010401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2002] [Revised: 04/16/2003] [Indexed: 05/24/2023]
Abstract
We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [Phys. Rev. Lett. 76, 1796 (1996)]] and in cavity QED [Nature (London) 403, 743 (2000)]]. The values of the Wigner functions of the underlying states at the origin of phase space are W(|0>)(0)=+1.75 for the vibrational ground state and W(|1>)(0)=-1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.
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Affiliation(s)
- P Lougovski
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
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Bertet P, Auffeves A, Maioli P, Osnaghi S, Meunier T, Brune M, Raimond JM, Haroche S. Direct measurement of the Wigner function of a one-photon Fock state in a cavity. PHYSICAL REVIEW LETTERS 2002; 89:200402. [PMID: 12443461 DOI: 10.1103/physrevlett.89.200402] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2002] [Indexed: 05/24/2023]
Abstract
We have measured the complete Wigner function W of the vacuum and of a single-photon state for a field stored in a high-Q cavity. This experiment implements the direct Lutterbach and Davidovich method [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)]] and is based on the dispersive interaction of a single circular Rydberg atom with the cavity field. The nonclassical nature of the single-photon field is exhibited by a region of negative W values. Extensions to other nonclassical cavity field states are discussed.
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Affiliation(s)
- P Bertet
- Laboratoire Kastler Brossel, Département de Physique de l'Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France
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25
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Klimov AB, Man$apos$ko OV, Man$apos$ko VI, Smirnov YF, Tolstoy VN. Tomographic representation of spin and quark states. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/29/312] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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26
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Santos MF, Solano E, de Matos Filho RL. Conditional large Fock state preparation and field state reconstruction in cavity QED. PHYSICAL REVIEW LETTERS 2001; 87:093601. [PMID: 11531566 DOI: 10.1103/physrevlett.87.093601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2001] [Indexed: 05/23/2023]
Abstract
We propose a scheme for producing large Fock states in cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.
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Affiliation(s)
- M F Santos
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil
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27
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Mancini S, Fortunato M, Tombesi P, D'Ariano GM. Toward a tomographic picture of a Bose-Einstein condensate. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2000; 17:2529-2535. [PMID: 11140513 DOI: 10.1364/josaa.17.002529] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The possibilities of applying tomographic techniques to a Bose-Einstein condensate to reconstruct its ground state are investigated by means of numerical simulations. Two situations for which the density-matrix elements can be retrieved from atom counting probabilities are considered. The methods presented here allow one to distinguish among various possible quantum states.
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Affiliation(s)
- S Mancini
- Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica, Università di Milano, Milan, Italy
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28
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Carmichael HJ, Castro-Beltran HM, Foster GT, Orozco LA. Giant violations of classical inequalities through conditional homodyne detection of the quadrature amplitudes of light. PHYSICAL REVIEW LETTERS 2000; 85:1855-1858. [PMID: 10970631 DOI: 10.1103/physrevlett.85.1855] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2000] [Indexed: 05/23/2023]
Abstract
Conditional homodyne detection is proposed as an extension of the intensity correlation technique introduced by Hanbury-Brown and Twiss [Nature (London) 177, 27 (1956)]. It detects giant quadrature amplitude fluctuations for weakly squeezed light, violating a classical bound by orders of magnitude. Fluctuations of both quadrature amplitudes are anomalously large. The squeezed quadrature also exhibits an anomalous phase.
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Affiliation(s)
- HJ Carmichael
- Abteilung fur Quantenphysik, Universitat Ulm, D-89069 Ulm, Germany
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29
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Vogel W. Nonclassical states: An observable criterion. PHYSICAL REVIEW LETTERS 2000; 84:1849-1852. [PMID: 11017643 DOI: 10.1103/physrevlett.84.1849] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/1999] [Revised: 07/28/1999] [Indexed: 05/23/2023]
Abstract
An observable criterion is derived that allows one to distinguish nonclassical states of the harmonic oscillator from those having a classical counterpart. A quantum state is shown to have no classical counterpart if and only if the characteristic functions of the quadrature distributions or the s-parametrized phase-space distributions exhibit a slower decay than for the ground state of the oscillator. This renders it possible to experimentally check the failure of the P function to be a probability measure.
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Affiliation(s)
- W Vogel
- Arbeitsgruppe Quantenoptik, Fachbereich Physik, Universitat Rostock, Universitatsplatz 3, D-18051 Rostock, Germany
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30
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Wineland DJ, Monroe C, Meekhof DM, King BE, Leibfried D, Itano WM, Bergquist JC, Berkeland D, Bollinger JJ, Miller J. Quantum state manipulation of trapped atomic ions. Proc Math Phys Eng Sci 1998. [DOI: 10.1098/rspa.1998.0168] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- D. J. Wineland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - C. Monroe
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. M. Meekhof
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - B. E. King
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Leibfried
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - W. M. Itano
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. C. Bergquist
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - D. Berkeland
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. J. Bollinger
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
| | - J. Miller
- Ion Storage Group, Time and Frequency Division, NIST, Div. 847, 325 Broadway, Boulder, CO 80303, USA
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Leibfried D, Meekhof DM, King BE, Monroe C, Itano WM, Wineland DJ. Experimental Determination of the Motional Quantum State of a Trapped Atom. PHYSICAL REVIEW LETTERS 1996; 77:4281-4285. [PMID: 10062500 DOI: 10.1103/physrevlett.77.4281] [Citation(s) in RCA: 119] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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33
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Wallentowitz S, Vogel W. Motional quantum states of a trapped ion: Measurement and its back action. PHYSICAL REVIEW A 1996; 54:3322-3334. [PMID: 9913855 DOI: 10.1103/physreva.54.3322] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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