Entanglement distillation

Entanglement distillation is the transformation of N copies of an arbitrary entangled state ${\displaystyle \rho }$ into some number of approximately pure Bell pairs, using only local operations and classical communication.

Quantum entanglement distillation can in this way overcome the degenerative influence of noisy quantum channels by transforming previously shared less entangled pairs into a smaller number of maximally entangled pairs.

The limits for entanglement dilution and distillation are due to Bennett, Bernstein, Popescu and Schumacher. Entanglement distillation protocols for pure states were originally presented in a paper by C. H. Bennett, H. Bernstein, S. Popescu, and B. Schumacher while Entanglement distillation protocols for mixed states were introduced by Bennett, Brassard, Popescu, Schumacher, Smolin and Wootters. Bennett, DiVincenzo, Smolin and Wootters established the connection to quantum error-correction in a ground-breaking paper published in August 1996 also in the journal of Physical Review, which has stimulated a lot of subsequent research.

A two qubit system can be written as a superposition of possible computational basis qubit states: ${\displaystyle |00\rangle ,|01\rangle ,|10\rangle ,|11\rangle }$, each with an associated complex coefficient ${\displaystyle \alpha \,\!}$:

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