TY - JOUR
T1 - Entanglement manipulation beyond local operations and classical communication
AU - Chitambar, Eric
AU - De Vicente, Julio I.
AU - Girard, Mark W.
AU - Gour, Gilad
N1 - Funding Information:
E.C. is supported by the National Science Foundation (NSF) Award No. 1914440. J.I.d.V. acknowledges support from the Spanish MINECO through Grants MTM2017-84098-P and MTM2017-88385-P and from the Comunidad de Madrid through grant QUITEMAD-CM P2018/TCS-4342. M.G. is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Institute for Advanced Research (CIFAR), and through funding provided to IQC by the Government of Canada. M.G. acknowledges further support from an Izaak Walton Killam Memorial Scholarship and an Alberta Innovates–Technology Futures (AITF) Graduate Student Scholarship. G.G. acknowledges support from NSERC.
Publisher Copyright:
© 2020 Author(s).
PY - 2020/4/1
Y1 - 2020/4/1
N2 - When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex, leaving many important physical problems unsolved. In this paper, we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and positive partial transpose (PPT)-preserving channels. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We first show that unlike LOCC, general non-entangling maps can be superactivated, in the sense that two copies of the same non-entangling map can, nevertheless, be entangling. On the single-copy level, we demonstrate that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and that every state can be converted into an LOCC-distillable state using operations belonging to any family of polytopes that approximate LOCC. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable channels. Finally, as an analog to k-positive maps, we introduce and analyze the set of k-non-entangling channels.
AB - When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex, leaving many important physical problems unsolved. In this paper, we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and positive partial transpose (PPT)-preserving channels. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We first show that unlike LOCC, general non-entangling maps can be superactivated, in the sense that two copies of the same non-entangling map can, nevertheless, be entangling. On the single-copy level, we demonstrate that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and that every state can be converted into an LOCC-distillable state using operations belonging to any family of polytopes that approximate LOCC. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable channels. Finally, as an analog to k-positive maps, we introduce and analyze the set of k-non-entangling channels.
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U2 - 10.1063/1.5124109
DO - 10.1063/1.5124109
M3 - Article
AN - SCOPUS:85083290026
SN - 0022-2488
VL - 61
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 4
M1 - 042201
ER -