Characterizing Bell nonlocality and EPR steering

Bell nonlocality and Einstein-Podolsky-Rosen(EPR) steering are very important quantum correlations in composite quantum systems. Bell nonlocality of a bipartite state is observed in some local quantum measurements, while EPR steering was first observed by Schr o¨dinger in the context of famous EPR paradox. In this paper, we discuss the Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity as well as the closedness of the sets of all Bell local states and all EPR unsteerable states, respectively. We also derive sufficient conditions for a state to be steerable; these conditions imply that Alice can steer Bob's state whenever Alice has two POV measurements such that the sets of Bob's normalized conditional states become two disjoint sets of pure states, or whenever she has one POV measurement such that Bob's normalized conditional states become a linearly independent set of pure states.     

Proofs of nonlocality without inequalities revisited

We discuss critically the so-called nonlocality without inequalities proofs for bipartite quantum states, we generalize them and we analyze their relation with the Clauser-Horne inequality.     

Steady-state teleportation fidelity and Bell nonlocality in dissipative environments

We investigate quantum teleportation and Bell nonlocality for two channel qubits coupled via the Heisenberg interaction and subject to two independent dissipative environments. Compared with the case of two uncoupled qubits, it is shown that the interaction Hamiltonian is beneficial for enhancing the teleportation fidelity and Bell nonlocality, and remarkably, it can also be used to create nonclassical teleportation fidelity and Bell nonlocality even from the initial product states. Moreover, the interaction Hamiltonian guarantees the generation of steady-state nonclassical teleportation fidelity, which is independent of the initial state and therefore one can take any state as the initial channel state.     

Tests of Bell inequalities

According to recent reports, the last loopholes in testing Bell's inequality are closed. It is argued that the really important task in this field has not been tackled yet and that the leading experiments claiming to close locality and detection efficiency loopholes, although making very significant progress, have conceptual drawbacks. The important task is constructing quantum devices which will allow winning games of certain correlated replies against any classical team. A novel game of this type is proposed.     

非简并双光子Jaynes-Cummings模型中贝尔非定域性的演化

基于赝自旋算符的关联所对应的贝尔算符期待值,研究了各种双模非经典态(纠缠相干态、对相干态以及双模压缩真空态)在非简并双光子Jaynes-Cummings模型中贝尔非定域性的动力学特性.结果表明:对于纠缠相干态,贝尔非定域性的演化与双模场平均光子数的大小息息相关;对于对相干态和双模压缩真空态,贝尔非定域性会在有限的时间内完全消失,之后又基本上复原到初始值,呈现出周期性振荡现象.     

Bell inequalities with auxiliary communication

What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties choose one of M two-outcome measurements and exchange 1 bit of information. We present the complete set of inequalities for M=2, and the complete set of inequalities for the joint correlation observable for M=3. We find that correlations produced by quantum theory satisfy both of these sets of inequalities. One bit of communication is therefore sufficient to simulate quantum correlations in both of these scenarios.     

Bell inequalities for graph states

We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.     

Bell inequalities for continuous-variable correlations

We derive a new class of correlation Bell-type inequalities. The inequalities are valid for any number of outcomes of two observables per each of n parties, including continuous and unbounded observables. We show that there are no first-moment correlation Bell inequalities for that scenario, but such inequalities can be found if one considers at least second moments. The derivation stems from a simple variance inequality by setting local commutators to zero. We show that above a constant detector efficiency threshold, the continuous-variable Bell violation can survive even in the macroscopic limit of large n. This method can be used to derive other well-known Bell inequalities, shedding new light on the importance of non-commutativity for violations of local realism.     

Correlations and efficiency: Testing the Bell inequalities

This paper examines the efficiency problem involved in experimental tests of so-called local hidden variables. It separates the phenomenological locality at issue in the Bell case from Einstein's different conception of locality, and shows how phenomenological locality also differs from the factorizability needed to derive the Bell inequalities in the stochastic case. It then pursues the question of whether factorizable, local models (or, equivalently, deterministic ones) exist for the experiments designed to test the Bell inequalities, thus rendering the experimental argument against them incomplete. This leads to an investigation of the so-called prism models and to new inequalities for a significant class of such models, inequalities that are testable even at the low efficiencies of the photon correlation experiments.Dedicated to David Bohm on the occasion of his 70th birthday, December 20, 1987.     

Ideals in ortholattices, Bell inequalities, and simultaneously definite properties

The notion of quasiboolean algebras (Bell and Clifton, 1995) is compared with related notions of semiprime ideals, commutator ideals, partial compatibility, joint distributions of observables, and Bell inequalities on orthomodular lattices. Some consequences of characterizations of simultaneously definite properties are derived.     

Generic tripartite Bell nonlocality sudden death under local phase noise

We definitively show, using an explicit and broadly applicable model, that local phase noise that is capable of eliminating state coherence only in the infinite-time limit is capable of eliminating nonlocality in finite time in three two-level systems prepared in the Bell-nonlocal tripartite states of the generic entanglement class.     

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.     

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.     

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     

Local hidden-variables theories violating Bell inequalities

It is shown that there is an implicit assumption in the derivation of the Bell inequalities which might be not true in some local hidden-variables models. That is the condition that one “photon” can excite either one atom or none.     

Weak objectification,joint probabilities,and Bell inequalities in quantum mechanics

The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.     

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.     

Qubit portrait of qudit states and Bell inequalities

A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. In view of the qubit-portrait method, the Bell inequalities for two qubits and two qutrits are discussed within the framework of the probability-representation of quantum mechanics. A semigroup of stochastic matrices is associated with tomographic-probability distributions of qubit and qutrit states. Bell-like inequalities are studied using the semigroup of stochastic matrices. The qudit-qubit map of tomographic probability distributions is discussed as an ansatz to provide a necessary condition for the separability of quantum states.