Vol.2 Special Issue
Dec 24, 2002 (print:
Dec. 31,
2002)
Editorial
(pp517518)
R. Cleve
Review and Research
Articles:
Simple
construction of quantum universal variablelength source coding (pp519529)
M. Hayashi and K.
Matsumoto
We simply construct a quantum universal variablelength source code
in which, independent of information source, both of the average error
and the probability that the coding rate is greater than the entropy
rate H(\overline{\rho}_p), tend to 0. If H(\overline{\rho}_p) is
estimated, we can compress the coding rate to the admissible rate H(\overline{\rho}_p)
with a probability close to 1. However, when we perform a naive
measurement for the estimation of H(\overline{\rho}_p), the input state
is demolished. By smearing the measurement, we successfully treat the
tradeoff between the estimation of H(\overline{\rho}_p) and the
nondemolition of the input state. Our protocol can be used not only for
the Schumacher's scheme but also for the compression of entangled
states.
Entangled graphs
(pp530539)
M. Plesch and V.
Buzek
We study how bipartite quantum entanglement (measured in terms of a
concurrence) can be shared in multiqubit systems. We introduce a
concept of the entangled graph such that each qubit of a
multipartite system is associated with a vertex while a bipartite
entanglement between two specific qubits is represented by an edge. We
prove that any entangled graph can be associated with a pure
state of a multiqubit system. We also derive bounds on the concurrence
for some weighted entangled graphs (the weight corresponds to the value
of concurrence associated with the given edge).
Multipartite
entanglement and hyperdeterminants
(pp540555)
A. Miyake and M.
Wadati
We classify multipartite entanglement in a unified manner, focusing on a
duality between the set of separable states and that of entangled
states. Hyperdeterminants, derived from the duality, are natural
generalizations of entanglement measures, the concurrence, 3tangle for
2, 3 qubits respectively. Our approach reveals how inequivalent
multipartite entangled classes of pure states constitute a partially
ordered structure under local actions, significantly different from a
totally ordered one in the bipartite case. Moreover, the generic
entangled class of the maximal dimension, given by the nonzero
hyperdeterminant, does not include the maximally entangled states in
Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits),
contrary to the widely known bipartite or 3qubit cases. It suggests
that not only are they never locally interconvertible with the majority
of multipartite entangled states, but they would have no grounds for the
canonical \(n\)partite entangled states. Our classification is also
useful for that of mixed states.
A simulated
photonnumber detector in quantum information processing
(pp556559)
K. Nemoto and S. Braunstein
A simulated photonnumber detection via homodyne detectors is considered
as a way to improve the efficiency near the singlephoton level of
communication. Current photonnumber detectors at infrared wavelengths
are typically characterized by their low detection efficiencies, which
significantly reduce the mutual information of a bosonic communication
channel. In order to avoid the inefficiency inherent in such direct
photonnumber detection, we evaluate an alternative setup based on
efficient dual homodyne detection. We show that replacing inefficient
direct detectors with homodynebased simulated direct detectors can
yield significant improvements, even near the singlephoton level of
operation. However we argue that there is a fundamental limit on the
ability of homodyne detection to simulate ideal photon number detection,
considering the exponential gap between quantum and classical computers.
This applies to arbitrarily complicated simulation strategies based on
homodyne detection.
Optimal
holonomic quantum gates
(pp560577)
A.O. Niskanen, M.
Nakahara, and M.M. Salomaa
We study the construction of holonomy
loops numerically in a realizationindependent model of holonomic
quantum computation. The aim is twofold. First, we present our technique
of finding the suitable loop in the control manifold for any onequbit
and twoqubit unitary gates. Second, we develop the formalism further
and add a penalty term for the length of the loop, thereby aiming to
minimize the execution time for the quantum computation. Our method
provides a general means by which holonomy loops can be realized in an
experimental setup. Since holonomic quantum computation is adiabatic,
optimizing with respect to the length of the loop may prove crucial.
Limit theorems and absorption
problems for quantum radom walks in one dimension
(pp578595)
N. Konno
In this paper we consider limit theorems, symmetry of
distribution, and absorption problems for two types of onedimensional
quantum random walks determined by $2 \times 2$ unitary matrices using
our PQRS method. The one type was introduced by Gudder in 1988, and the
other type was studied intensively by Ambainis et al. in 2001.
The difference between both types of quantum random walks is also
clarified.
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