Bell’s Theorem Without Inequalities and Only Two Distant Observers

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.     

Bell and Zeno

Bell's inequalities and related inequalities of Wigner, Clauser–Horne–Shimony–Holt, Accardi–Fedullo, Gudder–Zanghi, Herbert–Peres, Khrennikov, others, are shown to be contained within a general operator trigonometry developed by this author starting in 1967. These inequalities are improved here to useful quantum spin correlation identities. Secondly, the Zeno problems from quantum measurement theory are traced from early work by this author starting in 1974, to the present. A Zeno Alternative that stresses domain-theoretic properties as essential to distinguishing reversible from irreversible quantum evolutions is presented. PACS: 03.65.Ud, 03.65.Xp,02.30.Tb.     

State-Independent Proofs of Bell's Theorem Without Inequalities and Bell Inequality for Four-Qubit System

A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which possesses two qubits, is proposed. It is different from the other proofs in which there exists a fundamental requirement that certain specific suitable Bell states have been chosen. Moreover, in any non-ideal situation, a common Bell inequality independent of the choices of the 16-product states is derived, which is used to test the contradiction between quantum mechanics and local reality theory in the reach of current experimental technology.     

Entanglement between nuclear spin and field mode in GaAs semiconductors

In this paper we investigate entanglement between the nuclear spin and field mode in a GaAs semiconductor. The eigenfuctions of nuclear spin in the quantized external field are obtained and thus the von Neumann entropy is evaluated explicitly. It is shown that the von Neumann entropy monotonously increases with the spin-field coupling constant but monotonously decreases with the anisotropy energy.     

Nonlinear Inequalities and Entropy-Concurrence Plane

Nonlinear inequalities based on the quadratic Renyi entropy for mixed two-qubit states are characterized on the Entropy-Concurrence plane. This class of inequalities is stronger than Clauser-Horne-Shimony-Holt (CHSH) inequalities and, in particular, is violated “in toto” by the set of Type I Maximally-Entangled-Mixture States (MEMS I).     

Entanglement generation in trapped atoms

The two atoms in the ion trap are entangled by the interaction with an external excited atom. The evolution of the entanglement is analytically derived without the decoherence. Considering the spontaneous decay from the environment, the evolution of the entanglement is similar to the damping Rabi oscillation. The generation of entanglement is induced by the dipole-dipole type interaction of atoms. It is found that the entanglement of two trapped atoms is robust with the uniform interaction with the external atom. The collective spontaneous emission from the coupling between the atoms may enhance the entanglement.     

Quantum Logic, Probability, and Information: The Relation with the Bell Inequalities

We study the relation between the Bell inequalities—characteristic of noncontextual hidden variables theories of quantum mechanics—with quantum logic, quantum probability, and quantum information. The emphasis is on clarity and simplicity, although sometimes this implies a lack of mathematical rigor which, I hope, could be resolved without difficulty by the reader.     

Entanglement generation by electric field background

The quantum vacuum is unstable under the influence of an external electric field and decays into pairs of charged particles, a process which is known as the Schwinger pair production. We propose and demonstrate that this electric field can generate entanglement. Using the Schwinger pair production for constant and pulsed electric fields, we study entanglement for scalar particles with zero spins and Dirac fermions. One can observe the variation of the entanglement produced for bosonic and fermionic modes with respect to different parameters.     

Hidden Variables and Bell Inequalities on Quantum Logics

In the quantum logic approach, Bell inequalities in the sense of Pitowski are related with quasi hidden variables in the sense of Deliyannis. Some properties of hidden variables on effect algebras are discussed.     

Entanglement distribution over 150 km in wavelength division multiplexed channels for quantum cryptography

Granting information privacy is of crucial importance in our society, notably in fiber communication networks. Quantum cryptography provides a unique means to establish, at remote locations, identical strings of genuine random bits, with a level of secrecy unattainable using classical resources. However, several constraints, such as non‐optimized photon number statistics and resources, detectors' noise, and optical losses, currently limit the performances in terms of both achievable secret key rates and distances. Here, these issues are addressed using an approach that combines both fundamental and off‐the‐shelves technological resources. High‐quality bipartite photonic entanglement is distributed over a 150 km fiber link, exploiting a wavelength demultiplexing strategy implemented at the end‐user locations. It is shown how coincidence rates scale linearly with the number of employed telecommunication channels, with values outperforming previous realizations by almost one order of magnitude. Thanks to its potential of scalability and compliance with device‐independent strategies, this system is ready for real quantum applications, notably entanglement‐based quantum cryptography.

     

Bell inequalities for a sensible family of local hidden variable theories testable at low detection efficiency

A family of local models containing two angles as hidden variables is defined for experiments measuring polarization correlation of optical photons. Searching for the best model of the family, that is giving predictions most close to quantum mechanics, allows deriving Bell-type inequalities which may be tested with relatively low detection efficiency.     

From Quantum State Targeting to Bell Inequalities

Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally entangled states. The optimal solution of the game is used to derive a Bell inequality for two entangled qutrits. We argue that the nice properties of the inequality are direct consequences of the method of construction.     

Quantum theory does not require action at a distance

The question of whether or not the correlations predicted by quantum theory and actually observed in EPR-type experiments can be understood without assuming action at a distance is still controversial. The author's point of view, expressed by the title of this paper, is substantiated by the discussion of a specific example, and is defended against some recent criticism by H. P. Stapp.1. These predictions arenot exhausted by Eq. (1); see [9].     

Spatial Entanglement of Fermions in One-Dimensional Quantum Dots

The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree–Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.     

基于Bell态的三方量子密钥协商

提出了基于两粒子纠缠态的一个三方量子密钥协商协议. 方案中的三个参与者是完全对等的, 且对建立的共享密钥具有相同的贡献. 除此之外, 三方中的任何一方或两方都不能事先单独决定共享密钥. 安全分析表明本协议既能抵抗外部窃听者的攻击, 又能抵抗内部参与者攻击. 关键词： 量子密码学 量子密钥协商 Bell态     

Entanglement and the factorization-approximation

For a bi-partite quantum system defined in a finite dimensional Hilbert-space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement-operator, which is then shown to represent a non-conserved property for any bi-partite system and any type of interaction. This general relation does not exclude the existence of special initial product states, for which the entanglement remains small over some period of time, despite interactions. For this case we derive an approximation to the full Schr?dinger-equation, which allows the treatment of the composite systems in terms of product states. The induced error is estimated. In this factorization-approximation one subsystem appears as an effective potential for the other. A pertinent example is the Jaynes-Cummings model, which then reduces to the semi-classical rotating wave approximation. Received 8 June 2001     

Bell Inequalities and Separability of Uncommon Causes from the Setup Configuration

In the present paper the integration region Λ with more than one hidden variable is attributed to a pair of particles in the Bell's thought experiment as the local causal events in their common lightcone. Moreover, the possibility of uncommon causal events influencing the spin measurement is not ignored. Then, with regard to the separability of the influence of the uncommon events from configuration of the setup, and by relying on local realism and coherency, each of the Bell's inequality versions is obtained by measuring spin in three and four different directions. PACS numbers: 03.65.Ud 03.65.Ta.     

New loophole for the Einstein-Podolsky-Rosen paradox

Using the new concept of "stochastic gauge system", we describe a novel loophole to circumvent the Einstein-Podolsky-Rosen (EPR) paradox. We derive a "realistic" (i.e., classical) model, free from any paradox, which exactly emulates the spin EPR experiment. We conclude that Bell's inequalities are violated in classical physics as well, or, conversely that quantum mechanical theory is logically consistent with relativity.     

基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

Testing Bell inequalities in photonic crystals

We show how entangled atomic pairs can be prepared in order to test the Bell inequalities. The scheme is based on the interaction of the atoms with a highly localized field mode within a photonic crystal. The potential of using optically separated transitions and the stability of the entangled state to spontaneous emission could lead to the closure of the communication and the detection loopholes appearing in experiments so far. The robustness of the scheme against detector inefficiencies, the spread in the atomic velocities and the fact that the entangled pairs are not generated simultaneously is also studied. Received 31 July 2001 and Received in final form 30 November 2001