Detecting genuine multipartite entanglement of pure states with bipartite correlations

Abstract

Monogamy of bipartite correlations leads, for arbitrary pure multi-qubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable to exclude the possibility of k-separability.PACS numbers: 03.67.MnFor bipartite systems the phenomenon of quantum entanglement [1, 2] manifests itself in correlations. One might expect that genuinely n-partite entanglement gives rise to non-vanishing correlations between all n subsystems. This is incorrect, at least when correlations are quantified as average values of a product of local measurement results [3,4] (for a discussion on quantum correlations without classical correlations, see e.g. [5]). Thus, in order to detect genuine multipartite entanglement of certain states one has to rely on correlations between smaller number of subsystems [6].Here we discuss global features of multiparty qubit pure states, which can be deduced from their bipartite correlations. We shall use the property of monogamy of correlations [7]. Another approach has recently been put forward by Würflinger et al. [8] who have shown that some non-entangled reduced density operators can be linked with global entangled states.Monogamy of quantum correlations can be used for entanglement detection [9]. We will use it to derive a criterion for genuine multipartite entanglement. Monogamy was also employed in studies of quantum marginal problem, i.e. conditions for existence of a global quantum state given its marginals [10], security of quantum key distribution [11], and to show that correlations between macroscopic measurements ought to be classical [12]. It leads to efficient methods of solving strongly correlated multipartite quantum lattice systems [13].States of n qubits (two-level quantum systems) have density matrices of the following form:

Genuine N -partite entanglement without N -partite correlation functions

“…The left hand side of this equation is zero, as we showed in (14). Since both α k and α l are strictly positive numbers, we conclude that c 1 = 0.…”

“…Naturally one would wonder if it is possible to conclude the genuine multipartite entanglement from only non-zero bipartite correlation functions. This is important especially in view of entanglement witnesses which are combinations of correlation functions and therefore are insensitive to the vanishing correlation functions [11][12][13][14][15][16].…”

Uniform Entanglement Frames

“…Due to the importance of genuine entanglement, numerous approaches have been devoted to detecting genuinely multipartite entanglement. Among the influential ones, the methods using entanglement witness [2][3][4][5][6][7][8][9], generalized concurrence [10][11][12][13][14], and Bell-inequality [15] are very useful. Nevertheless, the problem of detecting genuinely entanglement is far from being solved.…”

Correlation-based entanglement criterion in bipartite multiboson systems

“…The main goal of our paper is to present correlation-based criteria for detection of this kind of entanglement. A correlation based approach [35][36][37][38] is desirable from an experimental point of view as they are most closely related to measured observables. However it cannot be directly applied to the case of multi-boson states, because it involves measurements performed on single localized particles.…”