Cost of Quantum Entanglement Simplified
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 informationtheoretically meaningful way. In particular, every previously defined entanglement measure bearing a precise informationtheoretic meaning is not known to be efficiently computable, or if it is efficiently computable, then it is not known to have a precise informationtheoretic meaning. In this Letter, we meet this challenge by introducing an entanglement measure that has a precise informationtheoretic 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 quantumphysical experiments.
 Publication:

Physical Review Letters
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevLett.125.040502
 arXiv:
 arXiv:2007.14270
 Bibcode:
 2020PhRvL.125d0502W
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 7 pages of main text, 20 pages of supplementary material, companion paper to arXiv:1809.09592