QIC Abstracts

 Vol.2 Special Issue Dec 24, 2002 (print: Dec. 31, 2002)
Editorial  (pp517-518)
        R. Cleve

Review and Research Articles: 
Simple construction of quantum universal variable-length source coding  (pp519-529)
        M. Hayashi and K. Matsumoto  
We simply construct a quantum universal variable-length 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 trade-off between the estimation of H(\overline{\rho}_p) and the non-demolition 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 (pp530-539)
        M. Plesch and V. Buzek  

We study how bi-partite quantum entanglement (measured in terms of a concurrence) can be shared in multi-qubit systems. We introduce a concept of the entangled graph such that each qubit of a multi-partite system is associated with a vertex while a bi-partite 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 multi-qubit 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 (pp540-555)
        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, 3-tangle 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 3-qubit 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 photon-number detector in quantum information processing  (pp556-559)
        K. Nemoto and S. Braunstein 
A simulated photon-number detection via homodyne detectors is considered as a way to improve the efficiency near the single-photon level of communication. Current photon-number 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 photon-number detection, we evaluate an alternative set-up based on efficient dual homodyne detection. We show that replacing inefficient direct detectors with homodyne-based simulated direct detectors can yield significant improvements, even near the single-photon 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  (pp560-577)
        A.O. Niskanen, M. Nakahara, and M.M. Salomaa
We study the construction of holonomy loops numerically in a realization-independent 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 one-qubit and two-qubit 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  (pp578-595)
        N. Konno
In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional 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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