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Does Svetlichny-box polytope fully characterize quantum correlations?

Chellasamy Jebarathinam

Published Jul 21, 2014• 0 citations
OpenAlex

Abstract

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.

Related papers

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

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

Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario

Chellasamy Jebarathinam, Debarshi Das, Suchetana Goswami +2 more

Abstract For a bipartite local quantum correlation, superlocality refers to the requirement for a larger dimension of the random variable in the classical simulation protocol than that of the quantum states that generate the correlations. In this work, we consider the classical simulation of local tripartite quantum correlations P among three parties and C . If at least one of the bipartitions , and is superlocal, then P is said to be absolutely superlocal, whereas if all three bipartitions are superlocal, then P is said to be genuinely superlocal. We present specific examples of genuine superlocality for tripartite correlations derived from three-qubit states. It is argued that genuine quantumness as captured by the notion of genuine discord is necessary for demonstrating genuine superlocality. Finally, the notions of absolute and genuine superlocality are also defined for multipartite correlations.

arXiv:1701.04363•Journal of Physics A Mathematical and Theoretical•Jul 9, 2018•8 citations

Complementarity in Genuine Nonlocality: A device independent outlook

Sasha Sami, Anubhav Chaturvedi, Indranil Chakrabarty

The notion of complementarity or mutually exclusiveness of physical phenomenon has always been of keen interest to the physicists. In this work we show that there exists a complementary relationship in terms of the genuine non-locality of a multipartite system vs. that of reduced subsystems. We further assert that the same is enforced due to no-signaling condition. To this end we consider Svetlichny games in a multiparty binary input and output scenario with a threshold value of the winning probability as a signature of genuine multiparty non locality. We analytically show that, in the Svetlichny games setup, there exists complementary relations between Svetlichny correlations of $n$ party and Svetlichny correlations of any subset of $k \leq n$ parties within the no-signaling framework. In other words, in general non local theories, the genuine multiparty non locality for multiparty systems comes at the cost of upper bounding the genuine multiparty non locality of the reduced subsystem. In addition to Svetlichny games we consider many other non local games like Mermin games, Bancal \emph{et al's} IP, Guess Your Neighbors Input game and provide numerical findings ( in case of no-signaling and quantum correlations ) in support of our main result.

•Mar 30, 2016•0 citations

Characterization of Quantum Correlations with Local Dimension Constraints and Its Device-Independent Applications

Miguel Navascués, de la, Torre Gonzalo, Tamás Vértesi

The future progress of semi-device independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns non-trivial bounds in all cases considered, allowing to study nonlocality scenarios with four measurement settings on one side and twelve (12) on the other in a normal desktop. In the tripartite case, we apply the hierarchy to derive a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than two, hence certifying three-dimensional tripartite entanglement in a device independent way. Finally, we show how the new method can be trivially modified to detect non-separable measurements in two-qubit scenarios.

•Jan 1, 2014•37 citations

Revealing hidden genuine tripartite nonlocality

Biswajit Paul, Kaushiki Mukherjee, Debasis Sarkar

Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely three-way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine three-way nonlocality remains a challenging problem as far as measurement context is concerned. Here we introduce an approach in this regard. We consider three tripartite quantum states, none of which is genuinely three-way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per measurement), but they can exhibit genuine three-way nonlocality when the initial states are subjected to stochastic local operations and classical communication. So, genuine three-way nonlocality is a resource which can be revealed by using a sequence of measurements.

arXiv:1512.08138•Physical Review A•Nov 7, 2016•9 citations
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.
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.
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.
Abstract For a bipartite local quantum correlation, superlocality refers to the requirement for a larger dimension of the random variable in the classical simulation protocol than that of the quantum states that generate the correlations. In this work, we consider the classical simulation of local tripartite quantum correlations P among three parties and C . If at least one of the bipartitions , and is superlocal, then P is said to be absolutely superlocal, whereas if all three bipartitions are superlocal, then P is said to be genuinely superlocal. We present specific examples of genuine superlocality for tripartite correlations derived from three-qubit states. It is argued that genuine quantumness as captured by the notion of genuine discord is necessary for demonstrating genuine superlocality. Finally, the notions of absolute and genuine superlocality are also defined for multipartite correlations.
The notion of complementarity or mutually exclusiveness of physical phenomenon has always been of keen interest to the physicists. In this work we show that there exists a complementary relationship in terms of the genuine non-locality of a multipartite system vs. that of reduced subsystems. We further assert that the same is enforced due to no-signaling condition. To this end we consider Svetlichny games in a multiparty binary input and output scenario with a threshold value of the winning probability as a signature of genuine multiparty non locality. We analytically show that, in the Svetlichny games setup, there exists complementary relations between Svetlichny correlations of nnn party and Svetlichny correlations of any subset of k≤nk \leq nk≤n parties within the no-signaling framework. In other words, in general non local theories, the genuine multiparty non locality for multiparty systems comes at the cost of upper bounding the genuine multiparty non locality of the reduced subsystem. In addition to Svetlichny games we consider many other non local games like Mermin games, Bancal \emph{et al's} IP, Guess Your Neighbors Input game and provide numerical findings ( in case of no-signaling and quantum correlations ) in support of our main result.
The future progress of semi-device independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns non-trivial bounds in all cases considered, allowing to study nonlocality scenarios with four measurement settings on one side and twelve (12) on the other in a normal desktop. In the tripartite case, we apply the hierarchy to derive a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than two, hence certifying three-dimensional tripartite entanglement in a device independent way. Finally, we show how the new method can be trivially modified to detect non-separable measurements in two-qubit scenarios.
Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely three-way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine three-way nonlocality remains a challenging problem as far as measurement context is concerned. Here we introduce an approach in this regard. We consider three tripartite quantum states, none of which is genuinely three-way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per measurement), but they can exhibit genuine three-way nonlocality when the initial states are subjected to stochastic local operations and classical communication. So, genuine three-way nonlocality is a resource which can be revealed by using a sequence of measurements.