alpha-logarithmic negativity

Abstract

© 2020 American Physical Society. The logarithmic negativity of a bipartite quantum state is a widely employed entanglement measure in quantum information theory due to the fact that it is easy to compute and serves as an upper bound on distillable entanglement. More recently, the $ąppa$ entanglement of a bipartite state was shown to be an entanglement measure that is both easily computable and has a precise information-theoretic meaning, being equal to the exact entanglement cost of a bipartite quantum state when the free operations are those that completely preserve the positivity of the partial transpose [Xin Wang and Mark M. Wilde, Phys. Rev. Lett. 125, 040502 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040502]. In this paper, we provide a nontrivial link between these two entanglement measures by showing that they are the extremes of an ordered family of $α$-logarithmic negativity entanglement measures, each of which is identified by a parameter $α$?1,∞. In this family, the original logarithmic negativity is recovered as the smallest with $α$=1, and the $p̨pa$ entanglement is recovered as the largest with $α$=∞. We prove that the $α$-logarithmic negativity satisfies the following properties: entanglement monotone, normalization, faithfulness, and subadditivity. We also prove that it is neither convex nor monogamous. Finally, we define the $α$-logarithmic negativity of a quantum channel as a generalization of the notion for quantum states, and we show how to generalize many of the concepts to arbitrary resource theories.

Publication
Physical Review A
Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.