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Characterizing quantum correlations in the nonsignaling framework
Quantum Physics · Submitted 20 May 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This decomposition allows us to isolate the origin of nonclassicality into three disjoint sources: a Popescu-Rohrlich box, a maximally local box that detects EPR-steering, and a classical correlation.
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The abstract, sentence by sentence
Quantum correlations forms a subset of the set of nonsignaling boxes. This allows us to characterize quantum correlations as a convex combination of the extremal boxes of the nonsignaling polytope which are Popescu-Rohrlich boxes (maximally nonlocal boxes) and local deterministic boxes. There exists multiple decomposition of quantum correlations in the context of the nonsignaling polytope. I find that the existence of Popescu-Rohrlich box decomposition for local boxes associates two notions of discord which capture nonclassicality of quantum correlations originating from Bell nonlocality and EPR-steering. I introduce, Bell and Mermin discord, and demonstrate that any bipartite nonsignaling box admits a three-way decomposition. This decomposition allows us to isolate the origin of nonclassicality into three disjoint sources: a Popescu-Rohrlich box, a maximally local box that detects EPR-steering, and a classical correlation. Interestingly, I show that all non-null quantum discord states which are neither classical-quantum states nor quantum-classical states can give rise to nonclassical correlations which have non-null Bell and/or Mermin discord for suitable noncommuting measurements. I introduce two notions of genuine discord, which are the generalizations of Bell and Mermin discord to the multipartite boxes, to characterize the presence of genuine nonclassicality in multipartite quantum correlations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Quantum correlations forms a subset of the set of nonsignaling boxes. | background 1.00 | 0.09 | 0.06 | asserted 1.00 |
| s1 | This allows us to characterize quantum correlations as a convex combination of the extremal boxes of the nonsignaling polytope which are Popescu-Rohrlich boxes (maximally nonlocal boxes) and local deterministic boxes. | background 0.40 | 0.35 | 0.18 | asserted 0.99 |
| s2 | There exists multiple decomposition of quantum correlations in the context of the nonsignaling polytope. | background 0.52 | 0.24 | 0.08 | asserted 1.00 |
| s3 | I find that the existence of Popescu-Rohrlich box decomposition for local boxes associates two notions of discord which capture nonclassicality of quantum correlations originating from Bell nonlocality and EPR-steering. | result 0.78 | 0.87 | 0.19 | asserted 1.00 |
| s4 | I introduce, Bell and Mermin discord, and demonstrate that any bipartite nonsignaling box admits a three-way decomposition. | contribution 0.96 | 0.92 | 0.18 | asserted 1.00 |
| s5 | This decomposition allows us to isolate the origin of nonclassicality into three disjoint sources: a Popescu-Rohrlich box, a maximally local box that detects EPR-steering, and a classical correlation. | interpretation 0.48 | 0.84 | 0.35 | asserted 1.00 |
| s6 | Interestingly, I show that all non-null quantum discord states which are neither classical-quantum states nor quantum-classical states can give rise to nonclassical correlations which have non-null Bell and/or Mermin discord for suitable noncommuting measurements. | result 0.98 | 0.87 | 0.15 | asserted 0.99 |
| s7 | I introduce two notions of genuine discord, which are the generalizations of Bell and Mermin discord to the multipartite boxes, to characterize the presence of genuine nonclassicality in multipartite quantum correlations. | contribution 1.00 | 0.93 | 0.22 | asserted 1.00 |
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Original abstract
Quantum correlations forms a subset of the set of nonsignaling boxes. This allows us to characterize quantum correlations as a convex combination of the extremal boxes of the nonsignaling polytope which are Popescu-Rohrlich boxes (maximally nonlocal boxes) and local deterministic boxes. There exists multiple decomposition of quantum correlations in the context of the nonsignaling polytope. I find that the existence of Popescu-Rohrlich box decomposition for local boxes associates two notions of discord which capture nonclassicality of quantum correlations originating from Bell nonlocality and EPR-steering. I introduce, Bell and Mermin discord, and demonstrate that any bipartite nonsignaling box admits a three-way decomposition. This decomposition allows us to isolate the origin of nonclassicality into three disjoint sources: a Popescu-Rohrlich box, a maximally local box that detects EPR-steering, and a classical correlation. Interestingly, I show that all non-null quantum discord states which are neither classical-quantum states nor quantum-classical states can give rise to nonclassical correlations which have non-null Bell and/or Mermin discord for suitable noncommuting measurements. I introduce two notions of genuine discord, which are the generalizations of Bell and Mermin discord to the multipartite boxes, to characterize the presence of genuine nonclassicality in multipartite quantum correlations.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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This division of the NS polytope allows us to obtain a 3-decomposition that any bipartite box with two binary inputs and two binary outputs can be decomposed into Popescu-Rohrlich (PR) box, a maximally local box, and a local box with BD and MD equal to zero.
What it cites · 10 sentences without a confident label
Uses the method or tool of 1 paper
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We will also apply the two bipartite measures, Bell and Mermin discord [ref] , to the marginal correlations.
Canonical decomposition of quantum correlations in the framework of generalized nonsignaling theories · Quantum correlations · 0.97
Cites as support 1 paper
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The polytope $𝒩_Tmm$ is quantum since its vertices are quantum realizable [ref] .
Range Theorems for Quantum Probability and Entanglement · Tsirelson bound · 0.99
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