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# Bell state

About: Bell state is a research topic. Over the lifetime, 3939 publications have been published within this topic receiving 117118 citations. The topic is also known as: Bell basis.

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Williams College

^{1}TL;DR: In this article, an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix was conjectured.

Abstract: The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

6,346 citations

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TL;DR: In this article, it was shown that the premisses of the Einstein-Podolsky-Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles.

Abstract: It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two‐particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin‐correlation and multiparticle interferometry examples are given of suitable three‐ and four‐particle arrangements, both at the gedanken and at the real experiment level.

1,896 citations

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TL;DR: A related but simpler EPR scheme is described and it is proved it secure against more general attacks, including substitution of a fake EPR source and the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.

Abstract: Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.

1,810 citations

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TL;DR: These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of

Abstract: We study the entanglement properties of a class of $N$-qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They also have a high persistency of entanglement which means that $\ensuremath{\sim}N/2$ qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of $lN/2$ qubits by simple measurements and classical communication.

1,429 citations

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TL;DR: Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type as mentioned in this paper, and some particular inequalities of this kind are proved in some particular cases of quantum correlations.

Abstract: Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail.

1,379 citations