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Quantum Mechanical Realization of a "PR-Box"

S. Marcovitch, Benni Reznik, Lev Vaidman A

Published Jan 18, 2006• 1 citation
OpenAlex

Abstract

We consider quantum ensembles which are determined by pre and post selection. Unlike the case of only pre selected ensembles, it is shown that in this case the probabilities for measurements outcomes at intermediate times respect causality only rarely: disconnected regions can generally use such ensembles to signal each other. We show that under restrictive conditions, there are certain non-trivial bi-partite ensembles which do respect causality. Some of these ensembles give rise to a violation of the CHSH inequality which exceeds the quantum maximal violation given by Cirel'son's bound ($B_{\\rm CHSH}\\le 2\\sqrt2$). We find that one of these causality respecting cases saturates the Popescu-Rohrlich bound for the maximal violation $B_{\\rm CHSH}\\le 4$. This case can be regarded as an a posteriori realization of ``super-correlations'' which has been recently termed as ``Popescu-Rohrlich box''.

Related papers

Quantum-mechanical realization of a Popescu-Rohrlich box

S. Marcovitch, Benni Reznik, Lev Vaidman A

We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson's bound ${B}_{\mathrm{CHSH}}\ensuremath{\le}2\sqrt{2}$ and obtains the Popescu-Rohrlich bound for the maximal violation, ${B}_{\mathrm{CHSH}}\ensuremath{\le}4$. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.

arXiv:quant-ph/0601122•Physical Review A•Feb 8, 2007•73 citations

Optical simulation of a Popescu-Rohrlich Box

Wen‐Jing Chu, Xiao-Lan Zong, Yang Ming +2 more

It is well known that the fair-sampling loophole in Bell test opened by the selection of the state to be measured can lead to post-quantum correlations. In this paper, we make the selection of the results after measurement, which opens the fair- sampling loophole too, and thus can lead to post-quantum correlations. This kind of result-selection loophole can be realized by pre- and post-selection processes within the "two-state vector formalism", and a physical simulation of Popescu-Rohrlich (PR) box is designed in linear optical system. The probability distribution of the PR has a maximal CHSH value 4, i.e. it can maximally violate CHSH inequality. Because the "two-state vector formalism" violates the information causality, it opens the locality loophole too, which means that this kind of results selection within "two-state vector formalism" leads to both fair- sampling loophole and locality loophole, so we call it a comprehensive loophole in Bell test. The comprehensive loophole opened by the results selection within "two-state vector formalism" may be another possible explanation of why post-quantum correlations are incompatible with quantum mechanics and seem not to exist in nature.

Scientific Reports•Jun 22, 2016•7 citations

Structure of quantum and classical implementations of the Popescu-Rohrlich box

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We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show that they all are entanglement-breaking channels, that they have certain block-diagonal structure, and we present some examples of such channels.

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CTC assisted PR box type correlation can lead to signaling

Indranil Chakrabarty, Tanumoy Pramanik, Arun Kumar Pati +1 more

It is known that there exist non-local correlations that respect no-signaling criterion, but violate Bell-type inequalities more than quantum-mechanical correlations. Such super quantum correlations were introduced as the Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three inputs and two/three outputs. We show that these super quantum correlations can lead to signaling when at least one of the input bit has access to a word line along a closed time-like curve.

arXiv:1107.2908•Jul 14, 2011•0 citations

CTC assisted PR box type correlation can lead to signaling

Indranil Chakrabarty, Tanumoy Pramanik, Arun Kumar Pati +1 more

It is known that there exist non-local correlations that respect no-signaling criterion, but violate Bell-type inequalities more than quantum-mechanical correlations. Such super quantum correlations were introduced as the Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three inputs and two/three outputs. We show that these super quantum correlations can lead to signaling when at least one of the input bit has access to a word line along a closed time-like curve.

Quantum Information and Computation•Oct 1, 2014•3 citations

Continuous-variable supraquantum nonlocality

Andreas Ketterer, Adrien Laversanne-Finot, Leandro Aolita

Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in postquantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures, instead of probability distributions, which involves a few technical subtleties. We show the existence of a class of supraquantum Gaussian correlations, which violate the Tsirelson bound of an adequate continuous-variable Bell inequality. We then introduce the continuous-variable version of the celebrated Popescu--Rohrlich (PR) boxes, as a limiting case of the above-mentioned Gaussian ones. Finally, we characterize the geometry of the set of continuous-variable no-signaling correlations. Namely, we show that that the convex hull of the continuous-variable PR boxes is dense in the no-signaling set. We also show that these boxes are extreme in the set of no-signaling behaviors and provide evidence suggesting that they are indeed the only extreme points of the no-signaling set. Our results lay the grounds for studying generalized-probability theories in continuous-variable systems.

arXiv:1707.05337•Physical Review A•Jan 31, 2018•7 citations
We consider quantum ensembles which are determined by pre and post selection. Unlike the case of only pre selected ensembles, it is shown that in this case the probabilities for measurements outcomes at intermediate times respect causality only rarely: disconnected regions can generally use such ensembles to signal each other. We show that under restrictive conditions, there are certain non-trivial bi-partite ensembles which do respect causality. Some of these ensembles give rise to a violation of the CHSH inequality which exceeds the quantum maximal violation given by Cirel'son's bound (BrmCHSHle2sqrt2B_{\\rm CHSH}\\le 2\\sqrt2BrmCHSH​le2sqrt2). We find that one of these causality respecting cases saturates the Popescu-Rohrlich bound for the maximal violation BrmCHSHle4B_{\\rm CHSH}\\le 4BrmCHSH​le4. This case can be regarded as an a posteriori realization of super-correlations'' which has been recently termed as Popescu-Rohrlich box''.
We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only preselected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain nontrivial bipartite ensembles which do satisfy causality. These ensembles give rise to a violation of the Clauser-Horne-Shimony-Holt inequality, which exceeds the maximal quantum violation given by Tsirelson's bound ${B}_{\mathrm{CHSH}}\ensuremath{\le}2\sqrt{2}$ and obtains the Popescu-Rohrlich bound for the maximal violation, ${B}_{\mathrm{CHSH}}\ensuremath{\le}4$. This may be regarded as an a posteriori realization of supercorrelations, which have recently been termed Popescu-Rohrlich boxes.
It is well known that the fair-sampling loophole in Bell test opened by the selection of the state to be measured can lead to post-quantum correlations. In this paper, we make the selection of the results after measurement, which opens the fair- sampling loophole too, and thus can lead to post-quantum correlations. This kind of result-selection loophole can be realized by pre- and post-selection processes within the "two-state vector formalism", and a physical simulation of Popescu-Rohrlich (PR) box is designed in linear optical system. The probability distribution of the PR has a maximal CHSH value 4, i.e. it can maximally violate CHSH inequality. Because the "two-state vector formalism" violates the information causality, it opens the locality loophole too, which means that this kind of results selection within "two-state vector formalism" leads to both fair- sampling loophole and locality loophole, so we call it a comprehensive loophole in Bell test. The comprehensive loophole opened by the results selection within "two-state vector formalism" may be another possible explanation of why post-quantum correlations are incompatible with quantum mechanics and seem not to exist in nature.
Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in postquantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures, instead of probability distributions, which involves a few technical subtleties. We show the existence of a class of supraquantum Gaussian correlations, which violate the Tsirelson bound of an adequate continuous-variable Bell inequality. We then introduce the continuous-variable version of the celebrated Popescu--Rohrlich (PR) boxes, as a limiting case of the above-mentioned Gaussian ones. Finally, we characterize the geometry of the set of continuous-variable no-signaling correlations. Namely, we show that that the convex hull of the continuous-variable PR boxes is dense in the no-signaling set. We also show that these boxes are extreme in the set of no-signaling behaviors and provide evidence suggesting that they are indeed the only extreme points of the no-signaling set. Our results lay the grounds for studying generalized-probability theories in continuous-variable systems.