SOME DERIVATIONS OF BELL’S INEQUALITY

1994 ◽  
Vol 29 (1) ◽  
pp. 63-105
Author(s):  
Kaj Børge Hansen
Keyword(s):  
Quantum Physics ◽  
Mathematical Problem ◽  
Hidden Variables ◽  
Quantum States ◽  
Valuable Insight ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Fixed Direction ◽  
Insight Into ◽  
Classical Picture

Eight derivations of Bell’s inequality are given. First a simple and concrete derivation is given drawing on the full strength of the two hypotheses of locality and hidden variables. Two attempts at deriving Bell’s inequality without locality are made. They fail, but give valuable insight into the form which nonlocality must take in quantum physics. Arguments are given against this form of nonlocality. Ontological ideas which allow separation, realism, and locality in quantum mechanics (QM) are indicated. In the following five derivations, a number of variants of the assumption of hidden variables are tried. Among the insights which these derivations give rise to are: (1) Particles cannot be assumed to have spin or polarisation values for as much as one fixed direction. (2) The classical picture of electromagnetic radiation is incompatible with QM. (3) Heisenberg’s idea of potentiality in elementary particles is incompatible with QM. (4) There is a weakest form of hidden variables, called realisability, which is sufficient to yield Bell’s inequality. (5) Quantum states cannot be identified with physical states. The mathematical problem of the integration of quantum states into physical states is nontrivial.

scholarly journals Reality or Locality? Proposed Test to Decide How Nature Breaks Bell's Inequality

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Johan Hansson
Keyword(s):  
Hidden Variables ◽  
Experimental Tests ◽  
Reconstruction Method ◽  
Bell’S Inequality ◽  
Objective Reality ◽  
Bell's Inequality ◽  
Set Up ◽  
First Time ◽  
Double Slit Experiment ◽  
Slit Experiment

Bell's theorem, and its experimental tests, has shown that the two premises for Bell's inequality—locality and objective reality—cannot both hold in nature, as Bell's inequality is broken. A simple test is proposed, which for the first time may decide which alternative nature actually prefers on the fundamental, quantum level. If each microscopic event is truly random (e.g., as assumed in orthodox quantum mechanics) objective reality is not valid whereas if each event is described by an unknown but deterministic mechanism (“hidden variables”) locality is not valid. This may be analyzed and decided by the well-known reconstruction method of Ruelle and Takens; in the former case no structure should be discerned, in the latter a reconstructed structure should be visible. This could in principle be tested by comparing individual “hits” in a double-slit experiment, but in practice a single fluorescent atom, and its (seemingly random) temporal switching between active/inactive states would possibly be better/more practical, easier to set up, observe, and analyze. However, only imagination limits the list of possible experimental setups.

scholarly journals Tripartite entanglement and quantum correlation

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Xingyu Guo ◽  
Chen-Te Ma
Keyword(s):  
Quantum Entanglement ◽  
Upper Bound ◽  
Pure State ◽  
Quantum Correlation ◽  
Quantum States ◽  
Bell’S Inequality ◽  
Tripartite Entanglement ◽  
Bell's Inequality ◽  
Unitary Transformations ◽  
Proper Diagnosis

Abstract We provide an analytical tripartite-study from the generalized R-matrix. It provides the upper bound of the maximum violation of Mermin’s inequality. For a generic 2-qubit pure state, the concurrence or R-matrix characterizes the maximum violation of Bell’s inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The R-matrix gives the maximum violation of Bell’s inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized R-matrix. The violation of Mermin’s inequality is not a proper diagnosis due to the non-monotonic behavior. We then classify 3-qubit quantum states. Each classification quantifies Quantum Entanglement by the total concurrence. In the end, we relate the experiment correlators to Quantum Entanglement.

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.

scholarly journals NOISE AND BELL'S INEQUALITY

2010 ◽  
Vol 09 (04) ◽  
pp. 423-426 ◽  
Author(s):  
DAVID K. FERRY ◽  
LASZLO B. KISH
Keyword(s):  
Bell Inequality ◽  
Hidden Variables ◽  
Strongly Correlated ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Bell's Inequality ◽  
Considerable Evidence ◽  
Classical Systems ◽  
Classical Waves ◽  
Classical Fields

To many, the idea of the EPR paradox and the possibility of local hidden variables were dismissed by the Bell inequality, although the central points of this argument have been around since the advent of quantum mechanics. Yet, there remains considerable evidence that this inequality can be violated even by classical systems. The question really is whether or not strongly correlated classical fields will also violate Bell's inequality. In a previous paper, it was shown that this was the case. Here, we ask the question as to just how much correlation in the classical waves is required to violate the inequality.

scholarly journals On the violation of Bell’s inequality for all non-product quantum states

2016 ◽  
Vol 14 (03) ◽  
pp. 1630003 ◽  
Author(s):  
Carlo Cafaro ◽  
Sean Alan Ali ◽  
Adom Giffin
Keyword(s):  
Quantum States ◽  
Particle Systems ◽  
Entangled State ◽  
Bell’S Inequality ◽  
Original Proof ◽  
Bell's Inequality

We present an explicit reexamination of Gisin’s 1991 original proof concerning the violation of Bell’s inequality for any pure entangled state of two-particle systems. Given the relevance of Gisin’s work, our analysis is motivated by pedagogical reasons and allows the straightening of a few mathematical points in the original proof that in no way change the physical conclusions reached by Gisin.

Study of the resistor material of an automotive spark plug by use of the charge-up effect along with elemental mapping in an electron microprobe

1991 ◽  
Vol 49 ◽  
pp. 742-743
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
J. S. Park ◽  
B. N. Juterbock
Keyword(s):  
Electron Microprobe ◽  
Present Report ◽  
Coated Sample ◽  
Valuable Insight ◽  
Elemental Mapping ◽  
Spark Plug ◽  
Carbon Coated ◽  
Electron Image ◽  
Electron Imaging ◽  
Insight Into

The electric and thermal properties of the resistor material in an automotive spark plug should be stable during its service lifetime. Containing many elements and many phases, this material has a very complex microstructure. Elemental mapping with an electron microprobe can reveal the distribution of all relevant elements throughout the sample. In this work, it is demonstrated that the charge-up effect, which would distort an electron image and, therefore, is normally to be avoided in an electron imaging work, could be used to advantage to reveal conductive and resistive zones in a sample. Its combination with elemental mapping can provide valuable insight into the underlying conductivity mechanism of the resistor.This work was performed in a CAMECA SX-50 microprobe. The spark plug used in the present report was a commercial product taken from the shelf. It was sectioned to expose the cross section of the resistor. The resistor was known not to contain the precious metal Au as checked on the carbon coated sample. The sample was then stripped of carbon coating and re-coated with Au.

Quantum Mechanical Interpretation of the Ultra-Low Energy Methyl-Rotation Dynamics in Porous Metal-Organic Frameworks Probed by Low-Frequency Vibrational Spectroscopy and ab initio Simulations

2018 ◽  
Author(s):  
Qi Li ◽  
Adam J. Zaczek ◽  
Timothy M. Korter ◽  
J. Axel Zeitler ◽  
Michael T. Ruggiero
Keyword(s):  
Ab Initio ◽  
Metal Organic Frameworks ◽  
Low Frequency ◽  
Rotor Dynamics ◽  
Quantum Mechanical ◽  
Valuable Insight ◽  
Void Space ◽  
Ab Initio Simulations ◽  
Metal Organic ◽  
Insight Into

<div>Understanding the nature of the interatomic interactions present within the pores of metal-organic frameworks</div><div>is critical in order to design and utilize advanced materials</div><div>with desirable applications. In ZIF-8 and its cobalt analogue</div><div>ZIF-67, the imidazolate methyl-groups, which point directly</div><div>into the void space, have been shown to freely rotate - even</div><div>down to cryogenic temperatures. Using a combination of ex-</div><div>perimental terahertz time-domain spectroscopy, low-frequency</div><div>Raman spectroscopy, and state-of-the-art ab initio simulations,</div><div>the methyl-rotor dynamics in ZIF-8 and ZIF-67 are fully charac-</div><div>terized within the context of a quantum-mechanical hindered-</div><div>rotor model. The results lend insight into the fundamental</div><div>origins of the experimentally observed methyl-rotor dynamics,</div><div>and provide valuable insight into the nature of the weak inter-</div><div>actions present within this important class of materials.</div>

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