Cost of quantum entanglement simplified
- URL: http://arxiv.org/abs/2007.14270v1
- Date: Tue, 28 Jul 2020 14:36:23 GMT
- Title: Cost of quantum entanglement simplified
- Authors: Xin Wang, Mark M. Wilde
- Abstract summary: We introduce an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state.
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.
- Score: 13.683637401785505
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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