Quantum Correlations in Nonlocal Boson Sampling

Abstract

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...

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

“…Shahandeh, Lund, and Ralph [46] have argued that since there is evidently something nonclassical going on in the RBS runs, something that is not captured by thinking in terms of the classical photon-number correlations in the state (4.1), this nonclassicality must be that of quantum optics, due to the nonclassical phase-space description of the state ρ CC , i.e., that it has a negative Glauber-Sudarshan P -function [47]. It is hard to credit this view, because the photon-number correlations in ρ CC are just a photon-mode way of describing the correlations with any classical device at Alice's end that selects number-state inputs to Bob's LON from a thermal probability distribution; such a classical device generally has no phase-space description.…”

Quasiprobability representation of quantum coherence

“…Note that X is defined only over real numbers R as the operator ix is not Hermitian forx =x † (x = 0). This space can be equipped with the Hilbert-Schmidt scalar product (x|ŷ) = tr(xŷ) (7) forx,ŷ ∈ X which yields the norm x = (x|x) 1/2 . For example, ρ 2 describes the purity of the state.…”

“…For example, quasiprobabilities can be applied to confirm fundamental predictions of quantum physics, such as nonlocality [2,3], macrorealism [4], and contextuality [5]. Moreover, negative quasiprobabilities serve as a resource for quantum information protocols [6,7].…”

Roughness as classicality indicator of a quantum state

“…The nonclassicality of quantum states phase space is also connected with measures based on information theory [70][71][72]. In reference [70], Ferraro et al show that there are distinct notions of classicality, and, under their considerations, that there exist quantum correlations that are not accessible by information-theoretic arguments.…”

“…In reference [70], Ferraro et al show that there are distinct notions of classicality, and, under their considerations, that there exist quantum correlations that are not accessible by information-theoretic arguments. Shahandeh et al [71] show that the only known classicality criterion violated by a non-local boson sampling protocol [73] is the phase-space nonclassicality. Baumgratz et al [74] investigated the quantifies of resource theory of quantum coherence.…”