3,894 research outputs found
Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes
Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum
convolutional codes are constructed from classical self-orthogonal
\F_4-linear and \F_2-linear convolutional codes, respectively. These
quantum convolutional codes have higher rate than comparable quantum block
codes or previous quantum convolutional codes, and are simple to decode. A
block single-error-correcting [9, 3, 3] tail-biting code is derived from the
unrestricted convolutional code, and similarly a [15, 5, 3] CSS-type block code
from the CSS-type convolutional code.Comment: 5 pages; to appear in Proceedings of 2005 IEEE International
Symposium on Information Theor
Convolutional and tail-biting quantum error-correcting codes
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to
4096 states and minimum distances up to 10 are constructed as stabilizer codes
from classical self-orthogonal rate-1/n F_4-linear and binary linear
convolutional codes, respectively. These codes generally have higher rate and
less decoding complexity than comparable quantum block codes or previous
quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same
rate and error-correction capability and essentially the same decoding
algorithms are derived from these convolutional codes via tail-biting.Comment: 30 pages. Submitted to IEEE Transactions on Information Theory. Minor
revisions after first round of review
Structured optical receivers to attain superadditive capacity and the Holevo limit
When classical information is sent over a quantum channel, attaining the
ultimate limit to channel capacity requires the receiver to make joint
measurements over long codeword blocks. For a pure-state channel, we construct
a receiver that can attain the ultimate capacity by applying a single-shot
unitary transformation on the received quantum codeword followed by
simultaneous (but separable) projective measurements on the
single-modulation-symbol state spaces. We study the ultimate limits of
photon-information-efficient communications on a lossy bosonic channel. Based
on our general results for the pure-state quantum channel, we show some of the
first concrete examples of codes and structured joint-detection optical
receivers that can achieve fundamentally higher (superadditive) channel
capacity than conventional receivers that detect each modulation symbol
individually.Comment: 4 pages, 4 figure
Regular and Singular Pulse and Front Solutions and Possible Isochronous Behavior in the Short-Pulse Equation: Phase-Plane, Multi-Infinite Series and Variational Approaches
In this paper we employ three recent analytical approaches to investigate the
possible classes of traveling wave solutions of some members of a family of
so-called short-pulse equations (SPE). A recent, novel application of
phase-plane analysis is first employed to show the existence of breaking kink
wave solutions in certain parameter regimes. Secondly, smooth traveling waves
are derived using a recent technique to derive convergent multi-infinite series
solutions for the homoclinic (heteroclinic) orbits of the traveling-wave
equations for the SPE equation, as well as for its generalized version with
arbitrary coefficients. These correspond to pulse (kink or shock) solutions
respectively of the original PDEs.
Unlike the majority of unaccelerated convergent series, high accuracy is
attained with relatively few terms. And finally, variational methods are
employed to generate families of both regular and embedded solitary wave
solutions for the SPE PDE. The technique for obtaining the embedded solitons
incorporates several recent generalizations of the usual variational technique
and it is thus topical in itself. One unusual feature of the solitary waves
derived here is that we are able to obtain them in analytical form (within the
assumed ansatz for the trial functions). Thus, a direct error analysis is
performed, showing the accuracy of the resulting solitary waves. Given the
importance of solitary wave solutions in wave dynamics and information
propagation in nonlinear PDEs, as well as the fact that not much is known about
solutions of the family of generalized SPE equations considered here, the
results obtained are both new and timely.Comment: accepted for publication in Communications in Nonlinear Science and
Numerical Simulatio
Symmetric M-ary phase discrimination using quantum-optical probe states
We present a theoretical study of minimum error probability discrimination,
using quantum- optical probe states, of M optical phase shifts situated
symmetrically on the unit circle. We assume ideal lossless conditions and full
freedom for implementing quantum measurements and for probe state selection,
subject only to a constraint on the average energy, i.e., photon number. In
particular, the probe state is allowed to have any number of signal and
ancillary modes, and to be pure or mixed. Our results are based on a simple
criterion that partitions the set of pure probe states into equivalence classes
with the same error probability performance. Under an energy constraint, we
find the explicit form of the state that minimizes the error probability. This
state is an unentangled but nonclassical single-mode state. The error
performance of the optimal state is compared with several standard states in
quantum optics. We also show that discrimination with zero error is possible
only beyond a threshold energy of (M - 1)/2. For the M = 2 case, we show that
the optimum performance is readily demonstrable with current technology. While
transmission loss and detector inefficiencies lead to a nonzero erasure
probability, the error rate conditional on no erasure is shown to remain the
same as the optimal lossless error rate.Comment: 13 pages, 10 figure
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