Related papers: The CHSH-type inequalities for infinite-dimensiona…
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of…
A generalization of the CHSH-Bell inequality to arbitrary many settings is presented. The singlet state of two spin $\half$ violates this inequality for all numbers of setting. In the limit of arbitrarily large number of settings, the…
In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an…
We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating…
The theorem developed by John Bell constituted the starting point of a revolution that translated a philosophical question about the nature of reality into the broad and intense field of research of the quantum information technologies. We…
We present a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states $\left|G_{abcd}\right >$ [Phys. Rev. A 65, 052112 (2002)] and several canonical four-qubit…
We consider a system of two spin-1/2 particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g. a collection of N independent spins), the two-particle system undergoes decoherence.…
A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell's…
Bell's theorem was a cornerstone for our understanding of quantum theory, and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been…
We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and…
We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient…
It was recently shown that the nonseparable density operators for a bipartite system are trace norm dense if either factor space has infinite dimension. We show here that non-local states -- i.e., states whose correlations cannot be…
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the…
In a general setting, we introduce a new bipartite state property sufficient for the validity of the perfect correlation form of the original Bell inequality for any three bounded quantum observables. A bipartite quantum state with this…
The usual derivation of the violation of Bell-type inequalities can be applied actually only for small distances between detectors. It does not take into account the dependence of the quantum mechanical wave function on space-time…
Bell inequalities have traditionally been used to demonstrate that quantum theory is nonlocal, in the sense that there exist correlations generated from composite quantum states that cannot be explained by means of local hidden variables.…
Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this…
We show that for pure and mixed states the problem of maximizing the correlation measure in the CHSH inequality reduces to maximizing the perimeter of a parallelogram enclosed by an ellipse characterized by the entanglement contained in the…
We construct the tripartite Bell-type inequalities of product states for l1-norm of coherence, relative entropy of coherence and skew information. Some three-qubit entangled states violate these inequalities. Particulary, the tripartite…