2003/12/31 by John Watrous · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physrevlett.93.010502
4 pages; major revisions, title changed, main result unchanged. Accepted for publication in PRL
arxiv created 2004/05/31 · openalex publication_date 2004/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A mixed quantum state \ensuremathρ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of \ensuremathρ into a single shared pair of qubits having high fidelity with the maximally entangled state |\ensuremathφ+\ensuremath⟩=(|00\ensuremath⟩+|11\ensuremath⟩)/√(2). In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer n there exists a state \ensuremathρ that is distillable, but, given n or fewer copies of \ensuremathρ, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.