Anonymous Quantum Nonlocality

Abstract

We show that for all n ≥ 3, an example of an n-partite quantum correlation that is not genuinely multipartite nonlocal but rather exhibiting anonymous nonlocality, that is, nonlocal but biseparable with respect to all bipartitions, can be obtained by locally measuring the n-partite GreenbergerHorne-Zeilinger (GHZ) state. This anonymity is a manifestation of the impossibility to attribute unambiguously the underlying multipartite nonlocality to any definite subset(s) of the parties, even though the correlation can indeed be produced by nonlocal collaboration involving only such subsets. An explicit biseparable decomposition of these correlations is provided for any partitioning of the n parties into two groups. Two possible applications of these anonymous GHZ correlations in the device-independent setting are discussed: multipartite secret sharing between any two groups of parties and bipartite quantum key distribution that is robust against nearly arbitrary leakage of information.Quantum correlations that violate a Bell inequality [1], a constraint first derived in the studies of local-hiddenvariable-theories, were initially perceived only as a counterintuitive feature with no classical analog. With the discovery of quantum information science, these intriguing correlations have taken the new role as a resource. For instance, in nonlocal games [2], the presence of Bellinequality-violating (hereafter referred as nonlocal) correlation signifies the usage of strategies that cannot be achieved using only shared randomness. They are also an indispensable resource in quantum information and communication tasks such as the reduction of communication complexity [3], the distribution of secret keys using untrusted devices [4,5], as well as the certification and expansion of randomness [6] etc. (see [7] for a review).Thus far, prior studies of quantum nonlocality have focussed predominantly on the bipartite setup. However, as with quantum entanglement [8,9], correlations between measurement outcomes can exhibit a much richer structure in the multipartite setup. Consider a multipartite Bell-type experiment with the i-th party's choice of measurement setting (input) denoted by x i = 0, 1 and the corresponding outcome (output) by a i = ±1. Already in the tripartite setting [10], quantum mechanics allow for correlations -a collection of joint conditional probability distributions P = {P ( a| x)} = {P (a 1 a 2 a 3 |x 1 x 2 x 3 )} -that cannot be reproduced even when a subset of the parties are allowed to share some nonlocal resource R [11,12].

Almost-quantum correlations and their refinements in a tripartite Bell scenario

“…Of course, in the light of the frameworks discussed in Refs. [49,50,54], the bounds that we have computed are also useful as deviceindependent [7] witnesses for nontrivial properties of the underlying quantum systems.…”

“…In particular, for all those Bell inequalities where there is a gap between its maximal quantum violation (column three) and the maximum value of Q T i 6 (columns eleven to thirteen), we can possibly use the extent to which the inequality is violated to conclude directly from the measurement statistics (i.e., in a device-independent [7] manner) the presence of a genuine tripartite entangled state. For example, with the appropriate bound in place, the quantum violation of inequality 7 [49] can be used as a device-independent witness for genuine tripartite entanglement [50]:…”

Quantifying multipartite nonlocality via the size of the resource

“…Then to prove that these correlations are not ( n 2 − 1) producible for the same set of resources, it was shown in Ref. [16] that except for even n with odd n 2 , these correlations are not 3-separable, i.e., cannot be reproduced by a separation of the n parties into three groups. As for R = Q, an MGS = n for odd n [16] follows from the fact that the corresponding correlation violates a device-independent witness for genuine n-partite entanglement [20,24] constructed from the Mermin-ArdehaliBelinskii-Klyshko (MABK) Bell expression [36,37].…”

“…However, relatively little is known [13,14] in the multipartite scenarios, where other interesting features are also present, such as the monogamy of nonlocal correlations (see, e.g., Refs. [7,15] and references therein) and the possibility of them being anonymous [16]. * florian.curchod@icfo.es † yliang@phys.ethz.ch Thus far, prior investigations on multipartite nonlocal correlations have focused predominantly on their m separability, namely, the possibility to reproduce them when the parties are separated into m groups [17]-specifically two groups [18][19][20][21][22][23]-and where the usage of some nonlocal resource R is only allowed within each group.…”

Phonon transport across a Si–Ge interface: The role of inelastic bulk scattering

“…Interfacial phonon transport has also been investigated using molecular dynamics (MD) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], atomistic Green's function (AGF) [22][23][24][25][26] and the Boltzmann transport equation (BTE) [27][28][29]. Each approach has its advantages and has been used to identify various phonon transport processes across heterojunctions.…”