Entanglement purification of unknown quantum states

Abstract

A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A {\bf 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 ${\rho }^{(N)}$ of the $N$ copies of the quantum system is exchangeable, one can write down a simple general expression for ${\rho }^{(N)}$. 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.

20 pages RevTeX 3.0 + 1 figure (encapsulated Postscript) Submitted to Physical Review A

References in corpus (2)

• Classical information and distillable entanglement
• Quantum Entanglement and the Maximum Entropy States from the Jaynes Principle

Cited by in corpus (14)

• One-and-a-half quantum de Finetti theorems
• A de Finetti representation for finite symmetric quantum states
• Entanglement distillation for three-particle W class states
• A de Finetti Representation Theorem for Quantum Process Tomography
• Entanglement purification for arbitrary unknown ionic states via linear optics
• Quantum theory from four of Hardy's axioms
• Universal entanglement concentration
• The Entropic Dynamics approach to Quantum Mechanics
• Entanglement distillation for W class states
• A Finite de Finetti Theorem for Infinite-Dimensional Systems
• Observables suitable for restricting the fidelity to multipartite maximally entangled states
• On the "Fake" Inferred Entanglement Associated with the Maximum Entropy Inference of Quantum States
• Additional information decreases the estimated entanglement using the Jaynes principle
• Entanglement purification of multi-mode quantum states