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Impossibility Criterion for Obtaining Pure Entangled States From Mixed States By Purifying Protocols

Ping-Xing Chen·Lin-Mei Liang·Cheng-Zu Li·Ming-Qiu Huang
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Abstract

Purifying noisy entanglement is a protocol which can increase the entanglement of a mixed state (as a source)at expense of the entanglement of others(as an ancilla)by collective measurement. A protocol with which one can get a pure entangled state from a mixed state is defined as purifying mixed states. We address a basic question: can one get a pure entangled state from a mixed state? We give a necessary and sufficient condition of purifying a mixed state by fit local operations and classical communication and show that for a class of source states and ancilla states in arbitrary bipartite systems purifying mixed states is impossible by finite rounds of purifying protocols. For $2\otimes 2$ systems, it is proved that arbitrary states cannot be purified by individual measurement. The possible application and meaning of the conclusion are discussed.

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Ping-Xing Chen, Lin-Mei Liang, Cheng-Zu Li, Ming-Qiu Huang. 2001-10-08. Impossibility Criterion for Obtaining Pure Entangled States From Mixed States By Purifying Protocols. https://doi.org/10.1103/physreva.65.012317

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