Detecting genuine multipartite continuous-variable entanglement

Abstract

We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multi-party multi-mode continuous-variable state. Their violations can be sufficient for genuine multipartite entanglement, provided the combinations contain both conjugate variables of all modes. Hence a complete state determination, for example by detecting the entire correlation matrix of a Gaussian state, is not needed.Comment: 13 pages, 3 figure

Systematic construction of genuine-multipartite-entanglement criteria in continuous-variable systems using uncertainty relations

“…In particular, we derive the unique family constituting single pairs of global n-mode position and momentum operators that simultaneously test entanglement in all possible bipartitions and also genuine n-partite entanglement. In the multipartite scenario, the criteria of van Loock and Furusawa [31] and also the criteria in [36][37][38] constitute particular cases of our results. In the bipartite scenario, we recover the most popular entanglement criteria [15-18, 22, 23].…”

“…In reference [36], the authors show that one of the criterion of van Loock and Furusawa, consisting of a single inequality for a proper non-local operator, is indeed a genuine multipartite entanglement criterion, and extend the criterion also for the product of variances. They also show how to adapt some of the criteria in [31], for three and four modes, in order to obtain genuine entanglement criteria. It is important to note that the criteria in [31,36] are based on uncertainty relations (UR) only for the variances of non-local linear observables (NLO) (i.e.…”

“…They also show how to adapt some of the criteria in [31], for three and four modes, in order to obtain genuine entanglement criteria. It is important to note that the criteria in [31,36] are based on uncertainty relations (UR) only for the variances of non-local linear observables (NLO) (i.e. linear combination of canonical conjugate local observables).…”

“…A first step in this direction for CV systems was made by van Loock and Furusawa [31] using a variance criterion to test full n−partite inseparability. These criteria do not require reconstruction of the covariance matrix, and for this reason they were preferred to test full n−partite inseparability in most of the CV multipartite states generated in the laboratory [10,11,13,[32][33][34].…”

Quantum-entangled light from localized emitters

“…The case of multipartite criteria based on second-order moments was studied earlier [32]; for its experimental application, see [33]. Consider a system of M spatial field modes in different propagation directions from the source, with positive frequency field operatorsÊ (+) j , j = 1, .…”