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| related topics |
| {error, code, errors} |
| {information, entropy, channel} |
| {states, state, optimal} |
| {alice, bob, state} |
| {key, protocol, security} |
| {state, phys, rev} |
| {group, space, representation} |
| {qubit, qubits, gate} |
| {state, states, coherent} |
| {algorithm, log, probability} |
| {theory, mechanics, state} |
| {entanglement, phys, rev} |
| {let, theorem, proof} |
| {equation, function, exp} |
| {phase, path, phys} |
| {state, states, entangled} |
|
Quantum Channel Capacity of Very Noisy Channels
David P. DiVincenzo, Peter W. Shor, John A. Smolin
abstract: We present a family of additive quantum error-correcting codes whose
capacities exceeds that of quantum random coding (hashing) for very noisy
channels. These codes provide non-zero capacity in a depolarizing channel for
fidelity parameters $f$ when $f> .80944$. Random coding has non-zero capacity
only for $f>.81071$; by analogy to the classical Shannon coding limit, this
value had previously been conjectured to be a lower bound. We use the method
introduced by Shor and Smolin of concatenating a non-random (cat) code within a
random code to obtain good codes. The cat code with block size five is shown to
be optimal for single concatenation. The best known multiple-concatenated code
we found has a block size of 25. We derive a general relation between the
capacity attainable by these concatenation schemes and the coherent information
of the inner code states.
- oai_identifier:
- oai:arXiv.org:quant-ph/9706061
- categories:
- quant-ph
- comments:
- 31 pages including epsf postscript figures. Replaced to correct
important typographical errors in equations 36, 37 and in text
- doi:
- 10.1103/PhysRevA.57.830
- arxiv_id:
- quant-ph/9706061
- created:
- 1997-06-27
- updated:
- 1998-11-03
Full article ▸
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