Local observables for entanglement detection of depolarized states

Abstract

We present an explicit construction of entanglement witnesses for depolarized states in arbitrary finite dimension. For infinite dimension we generalize the construction to twin-beams perturbed by Gaussian noises in the phase and in the amplitude of the field. We show that entanglement detection for all these families of states requires only three local measurements. The explicit form of the corresponding set of local observables (quorom) needed for entanglement witness is derived.

A study of LOCC-detection of a maximally entangled state using hypothesis testing

“…As a physical meaning, the optimal test is equivalent to optimal teleportation using a given state partially entangled, and the error probability is the same as the fidelity of the input and the output of the teleportation. It is also found that the test is equivalent to the extreme points of LOCC measurement described by Virmani and Plenio [27] and the entanglement witness given in [5]. Next, the result is generalized for the n-sample case.…”

“…The concept of entanglement witness is widely adopted, and there are many extensive arguments, especially, by making use of group symmetry. See, for example, theoretical works [20,9,5] and experiments [1]. However, in their arguments, analysis of statistical error is not sufficient.…”

Detection of Entanglement with Polarized Photons: Experimental Realization of an Entanglement Witness

“…Several methods have been proposed to assess the presence of entanglement for different types of quantum systems [8][9][10][11][12][13]. In particular, the socalled method of "entanglement witness" is a simple and efficient protocol that uses only a few local measurements [13]. In the present paper we report the first experimental implementation of an entanglement witness for polarizationentangled photons.…”

“…Since entanglement is an expensive resource-it cannot be distributed between distant parties by classical communication means-it becomes crucial to be able to detect it efficiently, with the minimum number of measurements. Several methods have been proposed to assess the presence of entanglement for different types of quantum systems [8][9][10][11][12][13]. In particular, the socalled method of "entanglement witness" is a simple and efficient protocol that uses only a few local measurements [13].…”

Nonseparable Werner states in spontaneous parametric down-conversion

“…For Werner states ρ W the method proposed in [25,41] leads to the following entanglement-witness operator:…”