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related topics |
{error, code, errors} |
{alice, bob, state} |
{let, theorem, proof} |
{algorithm, log, probability} |
{information, entropy, channel} |
{operator, operators, space} |
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The Minimum Distance Problem for Two-Way Entanglement Purification
Andris Ambainis, Daniel Gottesman
abstract: Entanglement purification takes a number of noisy EPR pairs 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_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) = -x \log_2 x - (1-x) \log_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 \geq 1 - (2t/n)
\log_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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0310097
- categories:
- quant-ph
- comments:
- 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
- doi:
- 10.1109/TIT.2005.862089
- arxiv_id:
- quant-ph/0310097
- journal_ref:
- IEEE Trans. Info. Theory vol. 52, issue 2, 748-753 (2006)
- created:
- 2003-10-14
- updated:
- 2005-10-13
Full article ▸
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