# Quantum analogues of the Bell inequalities. The case of two spatially separated domains

@article{Tsirelson1987QuantumAO, title={Quantum analogues of the Bell inequalities. The case of two spatially separated domains}, author={B. Tsirelson}, journal={Journal of Soviet Mathematics}, year={1987}, volume={36}, pages={557-570} }

One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and the classical correlation matrices is expressed] in terms of Grothendieck's known constant. It is also shown that the extremal quantum correlations characterize the Clifford algebra (i.e., canonical anticommutative relations).

#### 245 Citations

A histories perspective on characterizing quantum non-locality

- Physics
- 2014

We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum… Expand

A histories perspective on characterizing quantum nonlocality Dowker

- 2014

We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum… Expand

From Quantum Discord and Quantum Entanglement to Local Hidden Variable Models

- Physics
- 2015

We revisit the quantum discord, quantum entanglement and local hidden variable models in quantum mechanics, and present a kind of understanding of quantum states from the view of correlations given… Expand

Bounds on quantum nonlocality

- Mathematics, Physics
- 2017

One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no… Expand

Quantum limit of genuine tripartite correlations by bipartite extremality

- Physics
- 2020

The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identif...

On the Significance of the Quantum Mechanical Covariance Matrix

- Medicine, Computer Science
- Entropy
- 2018

This work shows that the extent of binary correlations in a general class of nonlocal theories can be characterized by the existence of a certain covariance matrix, and suggests that the Tsallis entropy with parameter q=1/2 is a natural operational measure of non-classicality. Expand

Geometry of the set of quantum correlations

- Physics
- 2018

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually… Expand

Locality and classicality: role of entropic inequalities

- Computer Science, Mathematics
- Quantum Inf. Process.
- 2015

The concept of classicality as the nonviolation of these classical inequalities by quantum states of several multiqubit systems is introduced and compared with the non Violation of Bell inequalities, that is, locality. Expand

Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

- Mathematics, Physics
- IEEE Transactions on Information Theory
- 2017

This work provides two lower bounds on the distance between a given unital quantum channel and the convex hull of unitary channels by employing techniques from quantum information and operator algebras, respectively and shows how to apply them to construct some explicit counterexamples to AQBC. Expand

Towards Grothendieck Constants and LHV Models in Quantum Mechanics

- Mathematics, Physics
- 2015

We adopt a continuous model to estimate the Grothendieck constants. An analytical formula to compute the lower bounds of Grothendieck constants has been explicitly derived for arbitrary orders, which… Expand

#### References

SHOWING 1-7 OF 7 REFERENCES

Quantum generalizations of Bell's inequality

- Mathematics
- 1980

Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of… Expand

Bell's inequalities and experimental verification of quantum correlations at macroscopic distances

- Physics
- 1984

In recent years the fulfillment of the inequalities established by Bell has been tested in different laboratories in the world. These inequalities make it possible to establish which of the… Expand

Bell's theorem. Experimental tests and implications

- Physics
- 1978

Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that are… Expand

Elements of the theory of representations

- Mathematics
- 1976

First Part. Preliminary Facts.- 1. Sets, Categories, Topology.- 1.1. Sets.- 1.2. Categories and Functors.- 1.3. The Elements of Topology.- 2. Groups and Homogeneous Spaces.- 2.1. Transformation… Expand

Constructive generalization of Bell’s inequalities

- Physics
- 1981

SummaryA process to construct all generalizations of Bell’s inequalities in a given experimental situation is presented. In view of the completeness thus obtained, we address a criticism to a very… Expand

Constantes de Grothendieck et fonctions de type positif sur les sphères

- Mathematics
- 1979

SoitL un espace de Banach reticule (“Banach lattice”) sur R. Si x1 ,..., xk EL on definit (x1” + ..’ + Xk2)1/2 = sup(‘ylxl + ... + c+& ; OLr ,..., CQ E R, a12 + ... + 01~~ = 1) (cette borne… Expand