Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

Kar, Guruprasad; Ghosh, Sibasish; Choudhary, Sujit K.; Banik, Manik

doi:10.3390/math4030052

Cited by 11 publications

(7 citation statements)

References 34 publications

(60 reference statements)

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“…Similar result follows for 'yes'-'no' questions that are performed based on shared randomness between Alice and Bob. To get more tangible results, we will use a well-know result from linear algebra that the dual of the vector space of bilinear forms is a tensor product of the original vector spaces, see [123] or Appendix C. Consider first the scenario where Alice applies 4. It then follows that the joint operation of Alice applying f A and Bob applying f B must behave as a bilinear functional on pairs of states.…”

Section: Bipartite Scenariosmentioning

confidence: 99%

“…• The nonlocal features of quantum theory, such as entanglement, steering and Bell inequality violations we investigated in GPTs [1][2][3][4][5][6][7][8]. One can, for example, construct theories which maximally violate the CHSH inequality and hence provide an implementation of the Popescu-Rohrlich (PR) boxes [9].…”

Section: Introductionmentioning

confidence: 99%

“…• Uncertainty relations [4,[11][12][13][14][15] and incompatibility of measurements and channels [5,[16][17][18][19][20][21][22][23][24][25][26] were investigated in GPTs. Incompatibility of measurements is a generalization of the non-commuting observables in quantum theory to an operational framework.…”

Section: Introductionmentioning

confidence: 99%

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General probabilistic theories: An introduction

Plávala

2021

Preprint

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We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories, such as the boxworld theory containing Popescu-Rohrlich boxes. We provide in-depth explanations of the basic concepts and elements of the framework of GPTs, and we also prove several well-known results. The review is self-contained and it is meant to provide the reader with consistent introduction to GPTs. Our tools mainly include convex geometry, but we also introduce diagrammatic notation and we often express equations via diagrams.

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Section: Bipartite Scenariosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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General probabilistic theories: An introduction

Plávala

2021

Preprint

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“…In fact, Rohrlich-Popescu proposed to axiomatize this limited Bell nonlocal behavior (along with relativistic causality) to derive quantum theory. Subsequently, several information and physical principles have been proposed to explain limited Bell nonlocality in quantum theory [6][7][8][9][10][11][12][13][14], and its connection with other quantum features has also been established [55][56][57][58][59][60][61]. In our work, we observe that the limited nonlocality without entanglement feature in quantum theory is owing to the continuity of the quantum state space structure which is presumed in axiomatic derivation of quantum theory either directly [29], or invoked through other assumptions such as "reversible transformation" [62] or "purification" [63].…”

Section: Dmentioning

confidence: 99%

Nonlocality without entanglement: Quantum theory and beyond

Bhattacharya

Saha

Guha

et al. 2020

Phys. Rev. Research

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Quantum nonlocality without entanglement (Q-NWE) captures nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded in the state ensemble that allows local preparation. In this Rapid Communication we show that the phenomena of NWE is not specific to quantum theory only, but rather a class of generalized probabilistic theories that can exhibit such behavior. In fact, several manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local discrimination, the notion of separable but locally unimplementable measurements arise generically in operational theories other than quantum theory. We propose a framework to compare the strength of NWE in different theories and show that such behavior in quantum theory is limited, suggesting a specific topological feature of quantum theory, namely, the continuity of state space structure. Our work adds the erstwhile missing foundational appeal to the study of NWE phenomena along with its information-theoretic relevance.

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“…It may be noted that principles like information causality (IC) [21] or macroscopic locality (ML) [22] do help us towards understanding physicality of some of the post-quantum correlations. Apart from these other conceptually different proposals have been introduced to single out the Tsirelson's bound [23][24][25][26][27]. But, till date, identifying the boundary between quantum correlations and post-quantum ones is not done completely and it remains an active area of research (see [28]).…”

Section: Introductionmentioning

confidence: 99%

Nonlocal correlations in a macroscopic measurement scenario

Kunkri¹,

Banik

Ghosh

2017

Phys. Rev. A

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Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystems. It is manifested theoretically as well as experimentally through violation of some local realistic inequality. On the other hand, classical behavior of all physical phenomena in the macroscopic limit gives a general intuition that any physical theory for describing microscopic phenomena should resemble classical physics in the macroscopic regime-the so-called macro-realism. In the 2-2-2 scenario (two parties, each performing two measurements, each measurement with two outcomes), contemplating all the no-signaling correlations, we characterize which of them would exhibit classical (local-realistic) behaviour in the macroscopic limit. Interestingly, we find correlations which at single copy level violate the Bell-Clauser-Horne-Shimony-Holt inequality by an amount less than optimal quantum violation (i.e., Cirel'son bound 2 √ 2), but in the macroscopic limit gives rise to a value which is higher than 2 √ 2. Such correlations are therefore not considered as physical. Our study thus provides a sufficient criterion to identify some of unphysical correlations.

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Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

Cited by 11 publications

References 34 publications

General probabilistic theories: An introduction

General probabilistic theories: An introduction

Nonlocality without entanglement: Quantum theory and beyond

Nonlocal correlations in a macroscopic measurement scenario

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