Tripartite entanglement and quantum correlation

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.

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How Does Nature Accomplish Spooky Action at a Distance?

Quanta ◽

10.12743/quanta.v7i1.82 ◽

2018 ◽

Vol 7 (1) ◽

pp. 111

Author(s):

Mani L. Bhaumik

Keyword(s):

Quantum Entanglement ◽

Quantum Correlation ◽

Quantum Nonlocality ◽

Quantum Mechanical ◽

Bell’S Inequality ◽

Bell's Inequality ◽

Nonlocal Correlations ◽

Satisfactory Account ◽

Nonlocal Quantum ◽

Action At A Distance

The enigmatic nonlocal quantum correlation that was famously derided by Einstein as "spooky action at a distance" has now been experimentally demonstrated to be authentic. The quantum entanglement and nonlocal correlations emerged as inevitable consequences of John Bell's epochal paper on Bell's inequality. However, in spite of some extraordinary applications as well as attempts to explain the reason for quantum nonlocality, a satisfactory account of how Nature accomplishes this astounding phenomenon is yet to emerge. A cogent mechanism for the occurrence of this incredible event is presented in terms of a plausible quantum mechanical Einstein–Rosen bridge.Quanta 2018; 7: 111–117.

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Conceptual Problems in Bell's Inequality and Quantum Entanglement

10.20944/preprints202002.0128.v1 ◽

2020 ◽

Author(s):

Ying-Qiu Gu

Keyword(s):

Quantum Theory ◽

Quantum Entanglement ◽

Classical Mechanics ◽

Bell State ◽

Bell’S Inequality ◽

Heisenberg Uncertainty Principle ◽

Bell's Inequality ◽

Micro Particles ◽

Wave Particle Duality ◽

New Interpretation

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

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SOME DERIVATIONS OF BELL’S INEQUALITY

Danish Yearbook of Philosophy ◽

10.1163/24689300_0290104 ◽

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.

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Paradoxes of measures of quantum entanglement and Bell's inequality violation in two-qubit systems

Journal of Computational Methods in Sciences and Engineering ◽

10.3233/jcm-2010-0338 ◽

2010 ◽

Vol 10 (3-6) ◽

pp. 501-512

Author(s):

Adam Miranowicz ◽

Bohdan Horst ◽

Andrzej Koper

Keyword(s):

Quantum Entanglement ◽

Bell’S Inequality ◽

Bell's Inequality

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Bell’s inequality, generalized concurrence and entanglement in qubits

International Journal of Modern Physics A ◽

10.1142/s0217751x19500325 ◽

2019 ◽

Vol 34 (06n07) ◽

pp. 1950032 ◽

Cited By ~ 1

Author(s):

Po-Yao Chang ◽

Su-Kuan Chu ◽

Chen-Te Ma

Keyword(s):

Upper Bound ◽

Entanglement Entropy ◽

Qubit State ◽

Bell’S Inequality ◽

Bell's Inequality ◽

Qubit System ◽

Maximal Violation ◽

Topological Entanglement Entropy ◽

Qubit States

It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an [Formula: see text]-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several [Formula: see text]-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.

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

International Journal of Quantum Information ◽

10.1142/s0219749916300035 ◽

2016 ◽

Vol 14 (03) ◽

pp. 1630003 ◽

Cited By ~ 1

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.

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“Non-locality”

10.1093/oso/9780198714057.003.0004 ◽

2017 ◽

Author(s):

Richard Healey

Keyword(s):

Quantum Theory ◽

Quantum Entanglement ◽

Quantum States ◽

Entangled States ◽

Entangled Quantum States ◽

Action At A Distance ◽

Insight Into ◽

Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

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Quantum Information in Neural Systems

Symmetry ◽

10.3390/sym13050773 ◽

2021 ◽

Vol 13 (5) ◽

pp. 773

Author(s):

Danko D. Georgiev

Keyword(s):

Quantum Entanglement ◽

Quantum Coherence ◽

Quantum Physics ◽

Quantitative Measure ◽

Quantum States ◽

Quantum Evolution ◽

Einstein Relation ◽

Schmidt Decomposition ◽

The Central Nervous System ◽

The Individual

Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.

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