9,557 research outputs found
Efficient Approximation of Quantum Channel Capacities
We propose an iterative method for approximating the capacity of
classical-quantum channels with a discrete input alphabet and a finite
dimensional output, possibly under additional constraints on the input
distribution. Based on duality of convex programming, we derive explicit upper
and lower bounds for the capacity. To provide an -close estimate
to the capacity, the presented algorithm requires , where denotes the input alphabet size and
the output dimension. We then generalize the method for the task of
approximating the capacity of classical-quantum channels with a bounded
continuous input alphabet and a finite dimensional output. For channels with a
finite dimensional quantum mechanical input and output, the idea of a universal
encoder allows us to approximate the Holevo capacity using the same method. In
particular, we show that the problem of approximating the Holevo capacity can
be reduced to a multidimensional integration problem. For families of quantum
channels fulfilling a certain assumption we show that the complexity to derive
an -close solution to the Holevo capacity is subexponential or
even polynomial in the problem size. We provide several examples to illustrate
the performance of the approximation scheme in practice.Comment: 36 pages, 1 figur
Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels
The superactivation of zero-capacity quantum channels makes it possible to
use two zero-capacity quantum channels with a positive joint capacity for their
output. Currently, we have no theoretical background to describe all possible
combinations of superactive zero-capacity channels; hence, there may be many
other possible combinations. In practice, to discover such superactive
zero-capacity channel-pairs, we must analyze an extremely large set of possible
quantum states, channel models, and channel probabilities. There is still no
extremely efficient algorithmic tool for this purpose. This paper shows an
efficient algorithmical method of finding such combinations. Our method can be
a very valuable tool for improving the results of fault-tolerant quantum
computation and possible communication techniques over very noisy quantum
channels.Comment: 35 pages, 17 figures, Journal-ref: Information Sciences (Elsevier,
2012), presented in part at Quantum Information Processing 2012 (QIP2012),
v2: minor changes, v3: published version; Information Sciences, Elsevier,
ISSN: 0020-0255; 201
Remote State Preparation
Quantum teleportation uses prior entanglement and forward classical
communication to transmit one instance of an unknown quantum state. Remote
state preparation (RSP) has the same goal, but the sender knows classically
what state is to be transmitted. We show that the asymptotic classical
communication cost of RSP is one bit per qubit - half that of teleportation -
and becomes even less when transmitting part of a known entangled state. We
explore the tradeoff between entanglement and classical communication required
for RSP, and discuss RSP capacities of general quantum channels.Comment: 4 pages including 1 epsf figure; v3 has an additional author and
discusses relation to work of Devetak and Berger (quant-ph/0102123); v4
improves low-entanglement protocols without back communication to perform as
well as low-entanglement protocols with back communication; v5 (journal
version) has a few small change
Communicating over adversarial quantum channels using quantum list codes
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.Comment: 6 pages. Discussion expanded and more details provided in proofs. Far
less unclear than previous versio
Characterizing the performance of continuous-variable Gaussian quantum gates
The required set of operations for universal continuous-variable quantum
computation can be divided into two primary categories: Gaussian and
non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed
as a sequence of phase-space displacements and symplectic transformations.
Although Gaussian operations are ubiquitous in quantum optics, their
experimental realizations generally are approximations of the ideal Gaussian
unitaries. In this work, we study different performance criteria to analyze how
well these experimental approximations simulate the ideal Gaussian unitaries.
In particular, we find that none of these experimental approximations converge
uniformly to the ideal Gaussian unitaries. However, convergence occurs in the
strong sense, or if the discrimination strategy is energy bounded, then the
convergence is uniform in the Shirokov-Winter energy-constrained diamond norm
and we give explicit bounds in this latter case. We indicate how these
energy-constrained bounds can be used for experimental implementations of these
Gaussian unitaries in order to achieve any desired accuracy.Comment: v3: 26 pages, 10 figures, final version accepted for publication in
Physical Review Researc
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