Entanglement purification of unknown quantum states

Journal Article · Sun Apr 01 04:00:00 EDT 2001 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.63.042309· OSTI ID:40206040

Brun, Todd A; Caves, Carlton M; Schack, Ru''diger

A concern has been expressed that ''the Jaynes principle can produce fake entanglement'' [R. Horodecki , Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state {rho}{sup (N)} of the N copies of the quantum system is exchangeable, one can write down a simple general expression for {rho}{sup (N)}. By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.

• Sponsoring Organization: (US)
• OSTI ID: 40206040
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 63; ISSN 1050-2947
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ENTROPY
EXPECTATION VALUE
PURIFICATION