Bell’s Theorem, Quantum Theory and Conceptions of the Universe

Kafatos, M.

doi:10.1007/978-94-017-0849-4

Cited by 134 publications

(22 citation statements)

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“…for any bipartite cut (bipartition) S|S, where S is a subset of A andS := A \ S denotes the rest of them. Probably the most well-known example of a GME state is the N -qubit Greenberger-Horne-Zeilinger state [35] defined as…”

Section: Preliminariesmentioning

confidence: 99%

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From unextendible product bases to genuinely entangled subspaces

Demianowicz

Augusiak

2018

Phys. Rev. A

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Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure state. Among CESs one finds a class of subspaces in which all vectors are not only entangled, but are genuinely entangled. Here we explore the connection between UPBs and such genuinely entangled subspaces (GESs) and provide classes of nonorthogonal UPBs that lead to GESs for any number of parties and local dimensions. We then show how these subspaces can be immediately utilized for a simple general construction of genuinely entangled states in any such multipartite scenario.

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Section: Preliminariesmentioning

confidence: 99%

“…The form of the numbers involved suggests conducting the remaining analysis using the representation of numbers in the base-d. Rewriting (35) using such representation we have…”

Section: A Monomial Coordinates Of Vectorsmentioning

confidence: 99%

From unextendible product bases to genuinely entangled subspaces

Demianowicz

Augusiak

2018

Phys. Rev. A

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“…1 (b), applies the Hadamard gate only on the first qubit, while there are controlled-not gates C (1,n) not on the n-th qubit, where the first qubit acts as the control. Instead of preparing the equally weighted superposition N times, this arrangement creates an entangled GHZ-state [55] using the eigenstates of σ z ,…”

Section: Noiseless Estimation With Entangled States -Obtaining Heimentioning

confidence: 99%

Precision Limits in Quantum Metrology with Open Quantum Systems

Haase¹,

Smirne²,

Kołodyński³

et al. 2016

Quantum Measurements and Quantum Metrology

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The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcome when using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment. We adopt a complementary approach, where we first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system's dissipative time evolution. We will show that although some forms of noise do render quantum systems to be standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

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“…To show this quantum feature, a well-known method is to test various of Bell inequalities [1,3], but the shortcoming of this approach can only provides a probabilistic demonstration of Bell nonlocality. By contrast, another significant approach to demonstrate Bell nonlocality by resorting to some logical contradictions(sometimes also called "Bell's theorem without inequalities" [4,5] or "nonlocality without inequalities" [6,7]) does not have such limitations. Demonstrations of Bell nonlocality by this method can be either deterministic or probabilistic.…”

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confidence: 99%

Perfect demonstration of Bell Nonlocality without Inequalities from Non-Perfect Correlations

Tang¹

2022

Preprint

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The all-versus-nothing proof of Bell nonlocality is a kind of mainstream demonstration of Bell's theorem without inequalities. Two species of such proofs, called the "always-type" all-versus-nothing proof and the "sometimes-type" all-versus-nothing proof, are both widely investigated. So far, almost all previous "always-type" all-versus-nothing proofs of Bell nonlocality are induced by perfect correlations from stabilizer states. Based on that, many people may customarily assume that only perfect correlations can give rise to "always-type" all-versus-nothing proofs. Here we present a kind of "always" type all-versus-nothing proof of Bell nonlocality from non-perfect correlations, clearing up this long-standing misconception. Our results may shed new light on the study of Bell nonlocality, and may have potential applications in some quantum information technologies.

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Bell’s Theorem, Quantum Theory and Conceptions of the Universe

Cited by 134 publications

References 0 publications

From unextendible product bases to genuinely entangled subspaces

From unextendible product bases to genuinely entangled subspaces

Precision Limits in Quantum Metrology with Open Quantum Systems

Perfect demonstration of Bell Nonlocality without Inequalities from Non-Perfect Correlations

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