scholarly journals On local-hidden-variable no-go theorems

2006 ◽  
Vol 84 (6-7) ◽  
pp. 633-638 ◽  
Author(s):  
A A Méthot
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Complete Theory ◽  
Variable Theory ◽  
Hidden Variable ◽  
Similarities And Differences ◽  
Hidden Variable Theories ◽  
03.65 Ud ◽  
Local Hidden Variable

The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow. PACS Nos.: 03.65.–w, 03.65.Ud, 03.65.Ta

scholarly journals KOCHEN–SPECKER THEOREM AND EXPERIMENTAL TEST ON HIDDEN VARIABLES

2000 ◽  
Vol 15 (18) ◽  
pp. 2813-2820 ◽  
Author(s):  
ADÁN CABELLO
Keyword(s):  
Quantum Mechanics ◽  
Experimental Test ◽  
Physical System ◽  
Hidden Variables ◽  
State System ◽  
Recent Proposal ◽  
Hidden Variable ◽  
Hidden Variable Theories

A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett.80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen–Specker theorem currently known [Phys. Lett.A212, 183 (1996)]. This proof contains eighteen yes-no questions about a four-dimensional physical system, combined in nine mutually incompatible tests. When these tests are considered as tests about a two-part two-state system, then quantum mechanics and noncontextual hidden variables make the same predictions for eight of them, but make different predictions for the ninth. Therefore, this ninth test would allow us to discriminate between quantum mechanics and noncontextual hidden-variable theories in a (gedanken) single run experiment.

scholarly journals Review on investigating the possibility of local hidden variable theories-quantum teleportation

2018 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Dorcas Attuabea Addo ◽  
Steven Abel ◽  
Richard Kwame Ansah ◽  
Isaac Nkrumah
Keyword(s):  
Single Particle ◽  
Quantum Teleportation ◽  
Entangled State ◽  
Bell’S Inequality ◽  
Variable Theory ◽  
Bell's Inequality ◽  
Hidden Variable ◽  
Hidden Variable Theories ◽  
Nonlocal Nature ◽  
Local Hidden Variable

The core of the paper was to investigate the possibility of local hidden variable theory and its application in quantum teleportation. We reviewed literature on the Bell's inequality which is necessary for quantum teleportation. Quantum teleportation utilises a single-particle entangled state which can be successfully achieved by the application of the locality assumption which leads to Bell's inequality. A violation of the Bell's inequality signifies the nonlocal nature of a single particle useful for quantum teleportation.

scholarly journals Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 185 ◽  
Author(s):  
Yeong-Cherng Liang ◽  
Yanbao Zhang
Keyword(s):  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Quantum Correlations ◽  
Ratio Method ◽  
Empirical Observation ◽  
Hidden Variable ◽  
Apparent Violation ◽  
Hidden Variable Theories ◽  
Experimental Trials ◽  
Local Hidden Variable

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.

NOVEL BELL INEQUALITIES FOR n QUBITS DISTRIBUTED BETWEEN m < n PARTIES

2009 ◽  
Vol 07 (supp01) ◽  
pp. 237-243
Author(s):  
ADÁN CABELLO
Keyword(s):  
Bell Inequalities ◽  
Hidden Variable ◽  
Hidden Variable Theories ◽  
Qubit States ◽  
Local Hidden Variable

We describe a method for obtaining m-partite Bell inequalities that are maximally violated by n-qubit states by an amount that grows exponentially with n (n > m). These inequalities, derived for states with perfect correlations, are, however, valid for all local hidden variable theories.

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