Quasiprobabilities for multipartite quantum correlations of light

Agudelo, Elizabeth; Sperling, Jan; Vogel, W.

doi:10.1103/physreva.87.033811

Cited by 48 publications

(67 citation statements)

References 42 publications

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“…As noted before, the input and output states in our protocol, as the only sources of any possible correlations, do not meet the quantumcorrelations criterion of quantum information, while, at the same time, showing nonclassical correlations. However, they fulfil the P -function nonclassicality criterion [29]. This observation leads us to the conclusion that negativity of P -function provides the resource for nonlocal BOSONSAMPLING and can be interpreted as a signature of true quantum correlations beyond entanglement and discord.…”

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confidence: 86%

“…(5) is a CC state with no quantum correlations from the quantum information viewpoint, due to the local orthogonality of the Fock states [20,21]. The FDTSV state has also other interesting features as shown by Agudelo et al [29]: its marginals,…”

mentioning

confidence: 94%

“…The reason is that there exist quantum states for which the marginal P -functions are regular probability distributions, while the joint P -function of the state contains negative regions. However, these examples range from highly entangled states, such as two-mode squeezed vacuum states, to fully separable ones [28,29]. Hence, while there are cases in which P -nonclassicality can be interpreted to be a signature of quantum correlations, in many other cases there is a question if such an interpretation is well-justified, or if the joint nonclassicality must be considered as a mere consequence of classical correlations?…”

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confidence: 99%

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Quantum Correlations in Nonlocal Boson Sampling

2017

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Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.Introduction.-Correlations play an undeniable role in our understanding of the physical world. In our macroscopic classical description of commonplace phenomena, classical physics and classical information theory are in perfect agreement in characterization and quantification of correlated events. At a microscopic level, where quantum theory is our best candidate for explaining phenomena, however, the situation is different. Our informational inspections of a quantum world, i.e., quantum information theory, is based on our intuition from classical information theory and classical probability theory, mostly the notion of quantum entropy [1, 2]. However, a discrepancy emerges when physical constraints are taken into account to distinguish between quantum physics and classical physics, hence splitting quantum information approach to correlations from that of quantum optics.In quantum optics it is common to study nonclassical features of bosonic systems in a quantum analogue of the classical phase space [3]. While in a classical statistical theory in phase-space the state of the system is represented by a probability distribution, the quantum phase-space distributions can have negative regions, and hence, fail to be legitimate probability distributions [4]. The negativities are thus considered as nonclassicality signatures. Within multipartite quantum states, the phase-space nonclassicality is tempted to be interpreted as quantum correlations, due to the fact that in a classical description of the joint system no such effects are present [5,6].The sharpest contrast between the definition of quantum correlations in quantum information science and that of quantum optics has been demonstrated very recently by Ferraro and Paris [7]. They showed that the two definitions from quantum information and quantum optics are maximally inequivalent, meaning that every quantum state which is classically correlated with respect to the quantum information definition of quantum correlations is nece...

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Quantum Correlations in Nonlocal Boson Sampling

2017

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“…The variance along the complex direction (mode)L i is 47) and the variance along the M − 1 complex directions (modes) orthogonal toL i is…”

Section: Characterization Runsmentioning

confidence: 99%

In situ characterization of linear-optical networks in randomized boson sampling

2020

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We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon counting, she obtains from Bob samples from the probability distribution of the RBS problem, a task that is believed to be classically hard to simulate. When Alice performs heterodyne measurements, she converts the experiment to a problem that is classically efficiently simulable, but more importantly, enables her to characterize a lossy LON on the fly, without Bob's knowing. We introduce and calculate the fidelity between the joint states shared by Alice and Bob after the ideal and lossy LONs as a measure of distance between the two LONs. Using this measure, we obtain an upper bound on the total variation distance between the ideal probability distribution for the RBS problem and the probability distribution achieved by a lossy LON. Our method displays the power of the entanglement of the two-mode squeezed-vacuum states: the entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on first-order coherence. Alice Classical channel Bob SPDC Classical channel SPDC SPDC LON Alice Bob C Q C Q C Q Q Q Q FIG. 1: M two-mode squeezed-vacuum states with the same squeezing parameter are generated by SPDC sources and shared between Alice and Bob. Bob inputs his modes to the LON, makes photon-counting measurements at the output of the LON, and sends the outcomes to Alice via a classical channel. Alice uses photon-counting measurements, denoted by Q, for the sampling runs of the RBS problem and makes heterodyne measurements, denoted by C, for characterizing Bob's LON. Because of the entanglement shared between the two parties, Alice can switch from a problem, based on photon counting, that is classically hard and not useful for characterization to a problem, based on heterodyne measurements, that is classically efficiently simulable and can be used for characterization.

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“…Furthermore, the quantum correlation has been generalized to continuous variable systems using Gaussian measurements for two-mode Gaussian states [21,22], and several experiments have been done [23][24][25][26][27][28][29][30]. It is worth noticing that non-discord like definitions of quantum correlations have been considered for continuous variable systems as well, related to their phase space representation, see [31,32] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Complete condition for nonzero quantum correlation in continuous variable systems

Zhang

Chen

et al. 2015

New J. Phys.

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Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker Q r . In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker Q r for all bipartite continuous variable states, and provide several examples including twomode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.

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Quasiprobabilities for multipartite quantum correlations of light

Cited by 48 publications

References 42 publications

Quantum Correlations in Nonlocal Boson Sampling

Quantum Correlations in Nonlocal Boson Sampling

In situ characterization of linear-optical networks in randomized boson sampling

Complete condition for nonzero quantum correlation in continuous variable systems

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