scholarly journals Simulation of the Bell inequality violation based on quantum steering concept

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohsen Ruzbehani
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Mathematical Formalism ◽  
Bell’S Inequality ◽  
Detector Efficiency ◽  
Bell's Inequality ◽  
Chsh Inequality ◽  
Quantum Steering ◽  
The Given

AbstractViolation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal influence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate effects, such as deficiency of detectors and polarizers, different value of photons in each run and so on. For example, it is demonstrated, when detector efficiency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efficiency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 $$\sqrt 2$$ 2 ) otherwise maximum violation will be limited to (1.5 $$\sqrt{2}$$ 2 ).

scholarly journals Buonomano against Bell: Nonergodicity or nonlocality?

2017 ◽  
Vol 15 (08) ◽  
pp. 1740010 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Bell Inequality ◽  
Quantum Measurements ◽  
Neutron Interferometry ◽  
Bell’S Inequality ◽  
Weak Mixing ◽  
Bell's Inequality

The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.

EPR and Bell Theorem

2020 ◽  
pp. 182-198
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
The Self ◽  
Experimental Results ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Bell Theorem ◽  
Chsh Inequality ◽  
Principle Of Complementarity

The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.

PROBING BELL'S INEQUALITY WITH CLASSICAL SYSTEMS

2010 ◽  
Vol 09 (04) ◽  
pp. 395-402 ◽  
Author(s):  
D. K. FERRY
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Hidden Variables ◽  
Optical Polarization ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Quantum Theories ◽  
Considerable Evidence ◽  
Classical Systems ◽  
Quantum Behavior

From the early days of quantum mechanics, there has been a discussion on the concept of reality, exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell inequality. Yet, there remains considerable evidence that this inequality can be violated even by classical systems, so that experiments showing quantum behavior and the violation of the inequality must be questioned. Here, we demonstrate that classical optical polarization experiments can be shown to violate the Bell inequality. Hence, such experiments cannot be used to distinguish between classical and quantum theories.

Bell's Inequalities for Any Spin

2003 ◽  
Vol 18 (28) ◽  
pp. 1931-1949
Author(s):  
V. M. González-Robles
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Point Of View ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Integer Spin ◽  
Half Integer ◽  
Locality Principle ◽  
Finite Integer ◽  
The Right

John Ju Sakurai's classical book in quantum mechanics makes a very illuminative presentation that studies entangled states in a two spin s=1/2 particles system in a singlet state. A Bell's inequality emerges as a consequence. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the nonlocal point of view of orthodox quantum mechanics. Following Sakurai's style we propose, by making natural induction, a generalization for Bell's inequality for any two spin-s particles in a singlet state (s integer or half-integer). This inequality is expressed as a function of a θ parameter, which is a measure of the angle between two possible directions in which the spin is measured. Besides the expression for this general inequality we have found that: (a) for any finite half-integer spin Bell's inequality is violated for some interval of the θ-parameter. The right limit of this interval is fixed and equal to π/2, while the left one comes closer and closer to this value as spin number grows. A function fit shows clearly that the size of this θ-interval over which Bell's inequality is violated diminishes asymptotically to zero as 1/s1/2; (b) an analogous behavior for any finite integer spin. For large spins the disagreement between Einstein's locality principle and the nonlocal point of view in orthodox quantum mechanics disappears.

scholarly journals GALOIS FIELD QUANTUM MECHANICS

2013 ◽  
Vol 27 (10) ◽  
pp. 1350064 ◽  
Author(s):  
LAY NAM CHANG ◽  
ZACHARY LEWIS ◽  
DJORDJE MINIC ◽  
TATSU TAKEUCHI
Keyword(s):  
Quantum Mechanics ◽  
Vector Space ◽  
Galois Field ◽  
Bell’S Inequality ◽  
Variable Theory ◽  
Bell's Inequality ◽  
Hidden Variable

We construct a discrete quantum mechanics (QM) using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser–Horne–Shimony–Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete QM cannot be reproduced with any hidden variable theory.

scholarly journals On Bell’s Inequality in PT-Symmetric Quantum Systems

2021 ◽  
Vol 3 (3) ◽  
pp. 417-424
Author(s):  
Sarang S. Bhosale ◽  
Biswanath Rath ◽  
Prasanta K. Panigrahi
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Systems ◽  
Inner Product ◽  
Bell’S Inequality ◽  
Standard Quantum ◽  
Bell's Inequality ◽  
Qubit System ◽  
Symmetric Quantum ◽  
No Signaling

Bell’s inequality is investigated in parity-time (PT) symmetric quantum mechanics, using a recently developed form of the inequality by Maccone [Am. J. Phys. 81, 854 (2013) ] , with two PT-qubits in the unbroken phase with real energy spectrum. It is shown that the inequality produces a bound that is consistent with the standard quantum mechanics even after using Hilbert space equipped with CPT inner product and therefore, the entanglement has identical structure with standard quantum mechanics. Consequently, the no-signaling principle for a two-qubit system in PT-symmetric quantum theory is preserved.

Sign in / Sign up

Export Citation Format

Share Document