2017/09/30 by Katarzyna Roszak, Łukasz Cywiński
Computer Science · Mathematics · Physics and Astronomy · #Bell state #Dephasing #LOCC #Mathematics #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Qubit #Separable space #Separable state #Squashed entanglement #Sudden death #quant-ph
paper · pdf · doi:10.1103/physreva.97.012306
published as Phys. Rev. A 97, 012306 (2018) · 10 pages, 1 figure
openalex created_date 2017/09/15 · arxiv created 2017/12/18 · openalex publication_date 2018/01/10 · arxiv updated 2018/01/17 · openalex updated_date 2026/08/05
We find that when a qubit initialized in a pure state experiences pure dephasing due to interaction with an environment, separable qubit-environment states generated during the evolution also have zero quantum discord with respect to the environment. What follows is that the set of separable states which can be reached during the evolution has zero volume, and hence, such effects as sudden death of qubit-environment entanglement are very unlikely. In the case of the discord with respect to the qubit, a vast majority of qubit-environment separable states is discordant, but in specific situations zero-discord states are possible. This is conceptually important since there is a connection between the discordance with respect to a given subsystem and the possibility of describing the evolution of this subsystem using completely positive maps. Finally, we use the formalism to find an exemplary evolution of an entangled state of two qubits that is completely positive, and occurs solely due to interaction of only one of the qubits with its environment (so one could guess that it corresponds to a local operation, since it is local in a physical sense), but which nevertheless causes the enhancement of entanglement between the qubits. While this simply means that the considered evolution is completely positive, but does not belong to local operations and classical communication, it shows how much caution has to be exercised when identifying evolution channels that belong to that class.