Cost of quantum entanglement simplified

TL;DR

This paper introduces a new entanglement measure that is both efficiently computable via semidefinite programming and has a clear information-theoretic interpretation as the cost to prepare entangled states with certain quantum operations.

Contribution

It proposes a novel entanglement measure with a precise information-theoretic meaning, computational efficiency, and desirable properties like additivity and faithfulness.

Findings

The measure is efficiently computable using semidefinite programming.

It has a clear interpretation as the cost to prepare entanglement.

It provides insights into the structure of quantum entanglement.

Abstract

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.