k-stretchability of entanglement, and the duality of k-separability and k-producibility

Abstract

The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement-like partial order, to build up their classification scheme. This general treatment reveals a new property, which we call $k$-stretchability, being sensitive in a balanced way to both the maximal size of correlated (or entangled) subsystems and the minimal number of subsystems uncorrelated with (or separable from) one another.

25 pages, 6 figures. v4: small fix in fig.1, does not affect results

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• Relating spin squeezing to multipartite entanglement criteria for particles and modes
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• Inherent quantum resources in stationary spin chains
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• Stretching the limits of multiparticle entanglement
• There exist infinitely many kinds of partial separability/entanglement
• Dicke subsystems are entangled
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• An exact Markovian decoherence dynamics of two interacting harmonic oscillators coupled to a bosonic heat bath