4 research outputs found
Cost of quantum entanglement simplified
Quantum entanglement is a key physical resource in quantum information
processing that allows for performing basic quantum tasks such as teleportation
and quantum key distribution, which are impossible in the classical world. Ever
since the rise of quantum information theory, it has been an open problem to
quantify entanglement in an information-theoretically meaningful way. In
particular, every previously defined entanglement measure bearing a precise
information-theoretic meaning is not known to be efficiently computable, or if
it is efficiently computable, then it is not known to have a precise
information-theoretic meaning. In this Letter, we meet this challenge by
introducing an entanglement measure that has a precise information-theoretic
meaning as the exact cost required to prepare an entangled state when two
distant parties are allowed to perform quantum operations that completely
preserve the positivity of the partial transpose. Additionally, this
entanglement measure is efficiently computable by means of a semidefinite
program, and it bears a number of useful properties such as additivity and
faithfulness. Our results bring key insights into the fundamental entanglement
structure of arbitrary quantum states, and they can be used directly to assess
and quantify the entanglement produced in quantum-physical experiments.Comment: 7 pages of main text, 20 pages of supplementary material, companion
paper to arXiv:1809.0959
Quantifying the unextendibility of entanglement
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states. First, we define the unextendible entanglement, a family of entanglement measures based on the concept of a state-dependent set of free states. The intuition behind these measures is that the more entangled a bipartite state is, the less entangled each of its individual systems is with a third party. Second, we demonstrate that the unextendible entanglement is an entanglement monotone under two-extendible quantum operations, including local operations and one-way classical communication as a special case. Normalization and faithfulness are two other desirable properties of unextendible entanglement, which we establish here. We further show that the unextendible entanglement provides efficiently computable benchmarks for the rate of exact entanglement or secret key distillation, as well as the overhead of probabilistic entanglement or secret key distillation