Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems

TL;DR

This paper derives inequalities to detect genuine multipartite steering in continuous variable systems, distinguishes between different types of steering, and demonstrates their creation, detection, and monogamy properties experimentally and theoretically.

Contribution

It introduces new inequalities for genuine N-partite steering detection, applicable beyond Gaussian states, and explores their creation, detection, and monogamy in continuous variable quantum systems.

Findings

Genuine N-partite steering inequalities are derived and experimentally confirmed.

Multipartite steering can be generated using squeezed states and beam splitters.

Monogamy relations for steering and entanglement distribution are analyzed.

Abstract

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we derive inequalities to detect a stricter genuine $N$-partite steering based on only one trusted site. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs, or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and the stricter definition) has been realised experimentally. Finally, we analyze how bipartite steering and entanglement is distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives advantage for quantum communication protocols.