We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even $d$ -dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even $d$-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.

arXiv:0803.3097Physical Review AJul 29, 200918 citations

Which states violate Bell's inequalities maximally?

Sandu Popescu, Rohrlich, D

Jan 1, 19920 citations

On the violation of Bell's inequality in quantum theory

Lawrence J. Landau

Physics Letters AFeb 1, 1987232 citations

Maximally entangled coherent states and strong violations of Bell-type inequalities

Christopher C. Gerry, Jihane Mimih, Adil Benmoussa

Recently, Wildfeuer et al. [Phys. Rev. A 76, 052101 (2007)] studied possible experiments demonstrating nonlocal correlation effects through the violation of various Bell-type inequalities by maximally path-entangled number states of the form $(|N⟩|0⟩+{e}^{i\ensuremath{\varphi}}|0⟩|N⟩)/\sqrt{2}$, the so-called $N00N$ states, and some strong violations were found. In this paper, we re-examine the same Bell-type inequalities with respect to maximally path-entangled coherent states of the form $\mathcal{N}({|\ensuremath{\alpha}⟩}_{a}{|0⟩}_{b}+{e}^{i\ensuremath{\Phi}}{|0⟩}_{a}{|\ensuremath{\alpha}\text{ }{e}^{i\ensuremath{\theta}}⟩}_{b})$. We find in many cases even stronger violations of the Bell-type inequalities than appear to be possible with the $N00N$ states.Recently, Wildfeuer et al. [Phys. Rev. A 76, 052101 (2007)] studied possible experiments demonstrating nonlocal correlation effects through the violation of various Bell-type inequalities by maximally path-entangled number states of the form $(|N⟩|0⟩+{e}^{i\ensuremath{\varphi}}|0⟩|N⟩)/\sqrt{2}$, the so-called $N00N$ states, and some strong violations were found. In this paper, we re-examine the same Bell-type inequalities with respect to maximally path-entangled coherent states of the form $\mathcal{N}({|\ensuremath{\alpha}⟩}_{a}{|0⟩}_{b}+{e}^{i\ensuremath{\Phi}}{|0⟩}_{a}{|\ensuremath{\alpha}\text{ }{e}^{i\ensuremath{\theta}}⟩}_{b})$. We find in many cases even stronger violations of the Bell-type inequalities than appear to be possible with the $N00N$ states.

Physical Review AAug 17, 200938 citations

The Einstein–Podolsky–Rosen State Maximally Violates Bell's Inequalities

Hans Halvorson

arXiv:quant-ph/0009007Letters in Mathematical PhysicsSep 1, 200020 citations

Maximal Violation of Bell Inequality for Any Given Two-Qubit Pure State

Yang Xiang

In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also gives the explicit values of maximal violation for any pure state. Finally we point out that any mixed states which can produce maximal violation of Bell inequality must have a maximal concurrence value.In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also gives the explicit values of maximal violation for any pure state. Finally we point out that any mixed states which can produce maximal violation of Bell inequality must have a maximal concurrence value.

arXiv:1006.3602Chinese Physics LettersDec 1, 20104 citations

We propose a Bell inequality for high-dimensional bipartite systems obtained by binning local measurement outcomes and show that it is tight. We find a binning method for even

d

-dimensional measurement outcomes for which this Bell inequality is maximally violated by maximally entangled states. Furthermore, we demonstrate that the Bell inequality is applicable to continuous variable systems and yields strong violations for two-mode squeezed states.

N00N

states, and some strong violations were found. In this paper, we re-examine the same Bell-type inequalities with respect to maximally path-entangled coherent states of the form $\mathcal{N}({|\ensuremath{\alpha}⟩}_{a}{|0⟩}_{b}+{e}^{i\ensuremath{\Phi}}{|0⟩}_{a}{|\ensuremath{\alpha}\text{ }{e}^{i\ensuremath{\theta}}⟩}_{b})$. We find in many cases even stronger violations of the Bell-type inequalities than appear to be possible with the

N00N

states.