Test of nonlocality for a continuous-variable state based on an arbitrary number of measurement outcomes

We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous-variable (CV) states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with complex ordering parameters, which can experimentally be determined via a local CV-qubit interaction. We demonstrate that CV systems can give higher violations of these Bell's inequalities than of the ones developed for two-outcome observables.     

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.     

Bell's theorem for general N-qubit states

We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.     

On an alternative interpretation of the bell inequalities

An alternative interpretation is discussed on which the Bell inequalities are not consequences of local realism and on which Einstein-Podolsky-Rosen-like experiments are no tests of the inequalities, because the Bell inequalities only need to be satisfied if all observables are measured jointly.     

Violation of Bell’s inequality for continuous-variable EPR states

We construct a wide class of bounded continuous variables observables that lead to violations of Bell inequalities for the EPR state and give an intuitive Wigner function explanation how to predetermine which operators wont ever exceed the bounds given by local theories. We show that as examples of such operators, we can use continuous-variable observables that satisfy the commutation relations for the Pauli matrices.     

Unsharp spin observables, non-locality and Fry, Walther and Li experiment

Recently it has been demonstrated that Bell inequalities for spin 1/2 particles must be modified if unsharp spin observables are considered, and furthermore, the modified Bell inequalities may not be violated by quantum mechanics if the observables are sufficiently unsharp. In case of massive particles there may be more imperfection than seems to appear in the photon EPR experiments. So the experiment proposed by Fry, Walther and Li can place experimental limits on the unsharpness of spin variables. It sheds new light on the much debated issues like non-local correlations in quantum mechanics.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.     

Equivalence between Bell inequalities and quantum minority games

We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality. We conclude the existence of direct correspondences between (i) the payoff rule and Bell inequalities, and (ii) the strategy and the choice of measured observables in evaluating these Bell inequalities. We also show that such a correspondence is unique to minority-like games.     

The Bell Theorem as a Special Case of a Theorem of Bass

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found 10 years earlier by Bass and stated in full generality by Vorob’ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.     

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.     

Loophole-free bell test for continuous variables via wave and particle correlations

We derive two classes of multimode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector efficiency, which makes a strong case for a loophole-free test.     

A model with cosmological Bell inequalities

We discuss the possibility of devising cosmological observables which violate Bell's inequalities. Such observables could be used to argue that cosmic scale features were produced by quantum mechanical effects in the very early universe. As a proof of principle, we propose a somewhat elaborate inflationary model where a Bell inequality violating observable can be constructed.     

On the implication of Bell’s probability distribution and proposed experiments of quantum measurement

In derivating of Bell’s inequalities, the probability distribution is supposed to be a function only of a hidden variable. We point out that the true implication of the probability distribution of Bell’s correlation function is the distribution of joint measurement outcomes on the two sides. It is therefore a function of both the hidden variable and the settings. In this case, Bell’s inequalities fail. Our further analysis shows that Bell’s locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, and hence violation of Bell’s inequalities cannot rule out the existence of local hidden variable. To explain the results of EPR-type experiments, we suppose that a polarization-entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any nonlocal influence on it. Then several experiments are suggested to reveal the components of the polarization-entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with the same quantum state behave the same under the same measuring conditions.     

Inequalities for nonideal correlation experiments

This paper addresses the inefficiency loophole in the Bell theorem. We examine factorizable stochastic models for the Bell inequalities, where we allow the detection efficiency to depend both on the hidden state of the measured system and also its passage through an analyzer. We show that, nevertheless, if the efficiency functions are symmetric between the two wings of the experiment, one can dispense with supplementary assumptions and derive new inequalities that enable the models to be tested even for highly inefficient experiments.     

Characterizing entanglement via uncertainty relations

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a family of bound entangled states and true multipartite entangled states can be detected. The inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits. We formulate an equivalent criterion in terms of covariance matrices. This allows us to apply criteria known from the regime of continuous variables to finite-dimensional systems.     

Configuration of separability and tests for multipartite entanglement in bell-type experiments

We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable n-particle density operators on an arbitrary dimensional space. This methodology enables us to derive a tight quadratic inequality as tests for full n-partite entanglement in various Bell-type correlation experiments on the systems that may not be identified as a collection of qubits, e.g., those involving photons measured by incomplete detectors. It is also proved that when the two measured observables are assumed to precisely anticommute, a stronger quadratic inequality can be used as a witness of full n-partite entanglement.     

Experimental detection of quantum entanglement

In this review, we introduce some methods for detecting or measuring entanglement. Several nonlinear entanglement witnesses are presented. We derive a series of Bell inequalities whose maximally violations for any multipartite qubit states can be calculated by using our formulas. Both the nonlinear entanglement witnesses and the Bell inequalities can be operated experimentally. Thus they supply an effective way for detecting entanglement. We also introduce some experimental methods to measure the entanglement of formation, and the lower bound of the convex-roof extension of negativity.     

Field Extension of Real Values of Physical Observables in Classical Theory can Help Attain Quantum Results

Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what would happen if physical observables are allowed to assume complex values. In this paper, we show that by allowing observables in the Bell inequality to take complex values, a classical physical theory can actually get the same upper bound of the Bell expression as quantum theory. Also, by extending the real field to the quaternionic field, we can puzzle out the GHZ problem using local hidden variable model. Furthermore, we try to build a new type of hidden-variable theory of a single qubit based on the result.