19,639 research outputs found
Quantum process reconstruction based on mutually unbiased basis
We study a quantum process reconstruction based on the use of mutually
unbiased projectors (MUB-projectors) as input states for a D-dimensional
quantum system, with D being a power of a prime number. This approach connects
the results of quantum-state tomography using mutually unbiased bases (MUB)
with the coefficients of a quantum process, expanded in terms of
MUB-projectors. We also study the performance of the reconstruction scheme
against random errors when measuring probabilities at the MUB-projectors.Comment: 6 pages, 1 figur
Mixed State Entanglement and Quantum Error Correction
Entanglement purification protocols (EPP) and quantum error-correcting codes
(QECC) provide two ways of protecting quantum states from interaction with the
environment. In an EPP, perfectly entangled pure states are extracted, with
some yield D, from a mixed state M shared by two parties; with a QECC, an arbi-
trary quantum state can be transmitted at some rate Q through a
noisy channel without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state (obtained
by sharing halves of EPR pairs through a channel ) yields a QECC on
with rate , and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
and that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for when is Bell-diagonal. While EPPs require classical communica-
tion, QECCs do not, and we prove Q is not increased by adding one-way classical
communication. However, both D and Q can be increased by adding two-way com-
munication. We show that certain noisy quantum channels, for example a 50%
depolarizing channel, can be used for reliable transmission of quantum states
if two-way communication is available, but cannot be used if only one-way com-
munication is available. We exhibit a family of codes based on universal hash-
ing able toachieve an asymptotic (or ) of 1-S for simple noise models,
where S is the error entropy. We also obtain a specific, simple 5-bit single-
error-correcting quantum block code. We prove that {\em iff} a QECC results in
high fidelity for the case of no error the QECC can be recast into a form where
the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also
http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82
pages latex including 19 postscript figures included using psfig macro
The capacity of the noisy quantum channel
An upper limit is given to the amount of quantum information that can be
transmitted reliably down a noisy, decoherent quantum channel. A class of
quantum error-correcting codes is presented that allow the information
transmitted to attain this limit. The result is the quantum analog of Shannon's
bound and code for the noisy classical channel.Comment: 19 pages, Submitted to Science. Replaced give correct references to
work of Schumacher, to add a figure and an appendix, and to correct minor
mistake
Resilience to time-correlated noise in quantum computation
Fault-tolerant quantum computation techniques rely on weakly correlated
noise. Here I show that it is enough to assume weak spatial correlations: time
correlations can take any form. In particular, single-shot error correction
techniques exhibit a noise threshold for quantum memories under spatially local
stochastic noise.Comment: 16 pages, v3: as accepted in journa
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