Entanglement manipulation and distillability beyond LOCC

Abstract

When a quantum system is distributed to spatially separated parties, it is\nnatural to consider how the system evolves when the parties perform local\nquantum operations with classical communication (LOCC). However, the structure\nof LOCC channels is exceedingly complex leaving many important physical\nproblems unsolved. In this paper we consider generalized resource theories of\nentanglement based on different relaxations to the class of LOCC. The behavior\nof various entanglement measures is studied under non-entangling channels, as\nwell as the newly introduced classes of dually non-entangling and\nPPT-preserving channels. In an effort to better understand the nature of LOCC\nbound entanglement, we study the problem of entanglement distillation in these\ngeneralized resource theories. We first show that unlike LOCC, general\nnon-entangling maps can be superactivated, in the sense that two copies of the\nsame non-entangling map can nevertheless be entangling. On the single-copy\nlevel, we demonstrate that every NPT entangled state can be converted into an\nLOCC-distillable state using channels that are both dually non-entangling and\nhaving a PPT Choi representation and that every state can be converted into an\nLOCC-distillable state using operations belonging to any family of polytopes\nthat approximate LOCC. We then turn to the stochastic convertibility of\nmultipartite pure states and show that any two states can be interconverted by\nany polytope approximation to the set of separable channels. Finally, as an\nanalog to $k$-positive maps, we introduce and analyze the set of\n$k$-non-entangling channels.\n