2003/10/31 by Andris Ambainis, Daniel Gottesman · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1109/tit.2005.862089
published as IEEE Trans. Info. Theory vol. 52, issue 2, 748-753 (2006) · 10 pages, LaTeX. v2: New title, minor corrections and clarifications, some new references. v3: One more small correction. v4: More small clarifications, final version to appear in IEEE Trans. Info. Theory
arxiv created 2005/10/13 · openalex publication_date 2006/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
Entanglement purification takes a number of noisy EPR pairs |00>+|11> and processes them to produce a smaller number of more reliable pairs. If this is done with only a forward classical side channel, the procedure is equivalent to using a quantum error-correcting code (QECC). We instead investigate entanglement purification protocols with two-way classical side channels (2-EPPs) for finite block sizes. In particular, we consider the analog of the minimum distance problem for QECCs, and show that 2-EPPs can exceed the quantum Hamming bound and the quantum Singleton bound. We also show that 2-EPPs can achieve the rate k/n=1-(t/n)log/sub 2/3-h(t/n)-O(1/n) (asymptotically reaching the quantum Hamming bound), where the EPP produces at least k good pairs out of n total pairs with up to t arbitrary errors, and h(x)=-xlog/sub 2/x-(1-x)log/sub 2/(1-x) is the usual binary entropy. In contrast, the best known lower bound on the rate of QECCs is the quantum Gilbert-Varshamov bound k/n/spl ges/1-(2t/n)log/sub 2/3-h(2t/n). Indeed, in some regimes, the known upper bound on the asymptotic rate of good QECCs is strictly below our lower bound on the achievable rate of 2-EPPs.