Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1407.3170

Canonical decomposition of quantum correlations in the framework of generalized nonsignaling theories

Chellasamy Jebarathinam

Published Jul 11, 2014• 2 citations
arXivHTMLPDF

Abstract

We introduce the measures, Bell discord (BD) and Mermin discord (MD), to characterize bipartite quantum correlations in the context of nonsignaling (NS) polytopes. These measures divide the full NS polytope into four regions depending on whether BD and/or MD is zero. 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. BD and MD quantify two types of nonclassicality of correlations arising from all quantum correlated states which are neither classical-quantum states nor quantum-classical states. BD and MD serve us the semi-device-independent witnesses of nonclassicality of local boxes in that nonzero value of these measures imply incompatible measurements and nonzero quantum discord only when the dimension of the measured states is fixed. The 3-decomposition serves us to isolate the origin of the two types of nonclassicality into a PR-box and a maximally local box which is related to EPR-steering, respectively. We consider a quantum polytope that has an overlap with all the four regions of the full NS polytope to figure out the constraints of quantum correlations.

DOI
10.48550/arxiv.1407.3170

Related papers

Characterizing quantum correlations in the nonsignaling framework

Chellasamy Jebarathinam

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.

arXiv:1605.06445•May 20, 2016•5 citations

Isolating genuine nonclassicality in tripartite quantum correlations

Chellasamy Jebarathinam

tions under the constraints of the HLHV model [3] and fully LHV model [15]. Analogous to genuine quantum discord [13], these measures detect the presence of genuine nonclassicality in Svetlichny-local correlations as well. We obtain a 3-decomposition that any correlation in the Svetlichny-box polytope which is a subpolytope of full NS polytope can be written as a convex combination of a Svetlichny-box, a maximally three-way contextual box, and a box which does not have Svetlichny and Mermin discord. Svetlichny and Mermin discord quantify the components of Svetlichny-box and three-way contextual box respectively in the 3-decomposition. Thus, Svetlichny and Mermin discord quantify genuine nonclassicality of Svetlichny-local quantum correlations originating from Svetlichny nonlocality and three-way contextuality respectively. We identify the set of genuinely nonclassical biseparable and separable three-qubit states using Svetlichny and Mermin discord.

•Jul 21, 2014•0 citations

On total correlations in a bipartite quantum joint probability distribution

Chellasamy Jebarathinam

We discuss the problem of separating the total correlations in a given quantum joint probability distribution into nonlocality, contextuality and classical correlations. Bell discord and Mermin discord which qunatify nonlocality and contextuality of quantum correlations are interpreted as distance measures in the nonsignaling polytope. A measure of total correlations is introduced to divide the total amount of correlations into a purely nonclassical part and a classical part. We show that quantum correlations satisfy additivity relations among these three measures.

arXiv:1410.1472•Oct 6, 2014•1 citation

Does Svetlichny-box polytope fully characterize quantum correlations?

Chellasamy Jebarathinam

In the nonsignaling framework, nonclassicality in correlation arising from two spatially separated input-output devices gets manifested, solely, through its \emph{nonlocal} behavior. Study of correlations based on this said feature is commonly known as local-nonlocal paradigm. While in two-party scenario correlations can be of only two types either local or nonlocal, the situation gets more involved for multi-party scenario, \emph{e.g.,} for tripartite scenario, correlations can be of three types: fully local, two-way local, and genuinely nonlocal. Nonsignaling correlations having quantum realization are termed physical. Fully local and certain quantum realizable two-way local tripartite correlations always have a quantum realization with tripartite biseparable states if there is no restriction on the local Hilbert-space dimensions. In this work, we study the quantum simulation of fully local and two-way local tripartite correlations with restricted local Hilbert-space dimensions, in particular we consider $\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2$ quantum systems. Interestingly, in this restricted simulation scenario we find that simulation of certain fully local and two-way local correlations necessarily requires \emph{genuine quantumness} in the three qubit states. This, going beyond the standard nonlocality paradigm, captures a new notion of genuine nonclassicality even in the fully local and two-way local correlations. To explore this newly introduced notion of genuine nonclassicality, we propose two quantities of interest, called \emph{Svetlichny strength} and \emph{Mermin strength}, and extensively study their properties.

•Jul 21, 2014•0 citations

Quantifying nonclassicality with local unitary operations

Sevag Gharibian

We propose a measure of nonclassical correlations in bipartite quantum states based on local unitary operations. We prove that the measure is nonzero if and only if the quantum discord is nonzero; this is achieved via a new characterization of zero discord states in terms of the state's correlation matrix. Moreover, our scheme can be extended to ensure that the same relationship holds even with a generalized version of quantum discord in which higher-rank projective measurements are allowed. We next derive a closed-form expression for our scheme in the cases of Werner states and $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional systems. The latter reveals that for $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states, our measure reduces to the geometric discord [Daki\ifmmode \acute{c}\else \'{c}\fi{} et al., Phys. Rev. Lett. 105, 190502 (2010)]. A connection to the Clauser-Horne-Shimony-Holt inequality is shown. We close with a characterization of all maximally nonclassical, yet separable, $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states of rank at most 2 (with respect to our measure).

arXiv:1202.1598•Physical Review A•Oct 8, 2012•46 citations

Bell measurement ruling out supraquantum correlations

Łukasz Czekaj, Michał Horodecki, Tomasz I. Tylec

The so-called bipartite nonsignaling boxes are systems whose statistics is constrained solely by the principle of no instantaneous signaling between distant locations. Such systems can exhibit much stronger correlations than those admitted by quantum mechanics. Inspired by the quantum logic approach of Tylec and Ku\ifmmode \acute{s}\else \'{s}\fi{} [J. Phys. A: Math. Theor. 48, 505303 (2015)], we consider nonsignaling boxes with three inputs per party and extend the set of measurements with just a single global measurement---one that mimics a quantum two-party Bell measurement. We then show that this seemingly mild extension completely rules out supraquantum correlations: the resulting system admits precisely quantum-mechanical correlations of two qubits. We also consider nonmaximally entangled measurements, obtaining interpolation between quantum and full nonsignaling theory. Our study paves the way to a general program of amending nonsignaling theories with some measurements inherited from quantum mechanics, leading to various interpolations between nonsignaling boxes and quantum mechanics.

arXiv:1802.09510•Physical Review A•Sep 24, 2018•8 citations
We introduce the measures, Bell discord (BD) and Mermin discord (MD), to characterize bipartite quantum correlations in the context of nonsignaling (NS) polytopes. These measures divide the full NS polytope into four regions depending on whether BD and/or MD is zero. 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. BD and MD quantify two types of nonclassicality of correlations arising from all quantum correlated states which are neither classical-quantum states nor quantum-classical states. BD and MD serve us the semi-device-independent witnesses of nonclassicality of local boxes in that nonzero value of these measures imply incompatible measurements and nonzero quantum discord only when the dimension of the measured states is fixed. The 3-decomposition serves us to isolate the origin of the two types of nonclassicality into a PR-box and a maximally local box which is related to EPR-steering, respectively. We consider a quantum polytope that has an overlap with all the four regions of the full NS polytope to figure out the constraints of quantum correlations.
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.
tions under the constraints of the HLHV model [3] and fully LHV model [15]. Analogous to genuine quantum discord [13], these measures detect the presence of genuine nonclassicality in Svetlichny-local correlations as well. We obtain a 3-decomposition that any correlation in the Svetlichny-box polytope which is a subpolytope of full NS polytope can be written as a convex combination of a Svetlichny-box, a maximally three-way contextual box, and a box which does not have Svetlichny and Mermin discord. Svetlichny and Mermin discord quantify the components of Svetlichny-box and three-way contextual box respectively in the 3-decomposition. Thus, Svetlichny and Mermin discord quantify genuine nonclassicality of Svetlichny-local quantum correlations originating from Svetlichny nonlocality and three-way contextuality respectively. We identify the set of genuinely nonclassical biseparable and separable three-qubit states using Svetlichny and Mermin discord.
We discuss the problem of separating the total correlations in a given quantum joint probability distribution into nonlocality, contextuality and classical correlations. Bell discord and Mermin discord which qunatify nonlocality and contextuality of quantum correlations are interpreted as distance measures in the nonsignaling polytope. A measure of total correlations is introduced to divide the total amount of correlations into a purely nonclassical part and a classical part. We show that quantum correlations satisfy additivity relations among these three measures.
In the nonsignaling framework, nonclassicality in correlation arising from two spatially separated input-output devices gets manifested, solely, through its \emph{nonlocal} behavior. Study of correlations based on this said feature is commonly known as local-nonlocal paradigm. While in two-party scenario correlations can be of only two types either local or nonlocal, the situation gets more involved for multi-party scenario, \emph{e.g.,} for tripartite scenario, correlations can be of three types: fully local, two-way local, and genuinely nonlocal. Nonsignaling correlations having quantum realization are termed physical. Fully local and certain quantum realizable two-way local tripartite correlations always have a quantum realization with tripartite biseparable states if there is no restriction on the local Hilbert-space dimensions. In this work, we study the quantum simulation of fully local and two-way local tripartite correlations with restricted local Hilbert-space dimensions, in particular we consider C2⊗C2⊗C2\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2C2⊗C2⊗C2 quantum systems. Interestingly, in this restricted simulation scenario we find that simulation of certain fully local and two-way local correlations necessarily requires \emph{genuine quantumness} in the three qubit states. This, going beyond the standard nonlocality paradigm, captures a new notion of genuine nonclassicality even in the fully local and two-way local correlations. To explore this newly introduced notion of genuine nonclassicality, we propose two quantities of interest, called \emph{Svetlichny strength} and \emph{Mermin strength}, and extensively study their properties.
We propose a measure of nonclassical correlations in bipartite quantum states based on local unitary operations. We prove that the measure is nonzero if and only if the quantum discord is nonzero; this is achieved via a new characterization of zero discord states in terms of the state's correlation matrix. Moreover, our scheme can be extended to ensure that the same relationship holds even with a generalized version of quantum discord in which higher-rank projective measurements are allowed. We next derive a closed-form expression for our scheme in the cases of Werner states and $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional systems. The latter reveals that for $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states, our measure reduces to the geometric discord [Daki\ifmmode \acute{c}\else \'{c}\fi{} et al., Phys. Rev. Lett. 105, 190502 (2010)]. A connection to the Clauser-Horne-Shimony-Holt inequality is shown. We close with a characterization of all maximally nonclassical, yet separable, $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states of rank at most 2 (with respect to our measure).
The so-called bipartite nonsignaling boxes are systems whose statistics is constrained solely by the principle of no instantaneous signaling between distant locations. Such systems can exhibit much stronger correlations than those admitted by quantum mechanics. Inspired by the quantum logic approach of Tylec and Ku\ifmmode \acute{s}\else \'{s}\fi{} [J. Phys. A: Math. Theor. 48, 505303 (2015)], we consider nonsignaling boxes with three inputs per party and extend the set of measurements with just a single global measurement---one that mimics a quantum two-party Bell measurement. We then show that this seemingly mild extension completely rules out supraquantum correlations: the resulting system admits precisely quantum-mechanical correlations of two qubits. We also consider nonmaximally entangled measurements, obtaining interpolation between quantum and full nonsignaling theory. Our study paves the way to a general program of amending nonsignaling theories with some measurements inherited from quantum mechanics, leading to various interpolations between nonsignaling boxes and quantum mechanics.