QIC Abstracts

 Vol.2 No.2 Feb. 15, 2002 (print: March 15, 2002)
Superposition, entanglement and quantum computation (pp97-116)
        T.M. Forcer, A.J.G. Hey, D.A. Ross and P.G.R. Smith
The paper examines the roles played by superposition and entanglement in quantum computing. The analysis is illustrated by discussion of a "classical" electronic implementation of Grover's quantum search algorithm. It is shown explicitly that the absence of multi-particle entanglement leads to exponentially rising resources for implementing such quantum algorithms.

Simulating arbitrary pair-interactions by a given Hamiltonian:
graph-theoretical bounds on the time-complexity  (pp117-132)
        P. Wocjan, D. Janzing and T. Beth
We consider a quantum computer consisting of n spins with an arbitrary but fixed pair-interaction Hamiltonian and describe how to simulate other pair-interactions by interspersing the natural time evolution with fast local transformations. Calculating the minimal time overhead of such a simulation leads to a convex optimization problem. Lower and upper bounds on the minimal time overhead are derived in terms of chromatic indices of interaction graphs and spectral majorization criteria. These results classify Hamiltonians with respect to their computational power.  For a specific Hamiltonian, namely \sigma_z\otimes\sigma_z-interactions between all spins, the optimization is mathematically equivalent to a separability problem of n-qubit density matrices. We compare the complexity defined by such a quantum computer with the usual gate complexity.

Universal simulation of Hamiltonians using a finite set of control operations  (pp133-150)
        P. Wocjan, M. Rotteler, D. Janzing and T. Beth
Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is possible to simulate an arbitrary bipartite interaction by a given one using such groups acting locally on the subsystems.

The quantum state of a laser field  (pp151-165)
        S.J. van Enk and C.A. Fuchs
Optical implementations of quantum communication protocols typically involve laser fields. However, the standard description of the quantum state of a laser field is surprisingly insufficient to understand the quantum nature of such implementations. In this paper, we give a quantum information-theoretic description of a propagating continuous-wave laser field and reinterpret various quantum-optical experiments in light of this. A timely example is found in a recent controversy about the quantum teleportation of continuous variables. We show that contrary to the claims of T. Rudolph and B.C. Sanders [Phys.  Rev.  Lett. {\bf 87}, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable quantum entanglement. Furthermore, we show that optical coherent states do play a privileged role in the description of propagating laser fields even though they cannot be ascribed such a role for the intracavity field.

NMR quantum information processing and entanglement (pp166-176)
        R. Laflamme, D. Cory, C. Negrevergne and L. Viola
In this essay we discuss the issue of quantum information and recent nuclear magnetic resonance (NMR) experiments. We explain why these experiments should be regarded as quantum information processing (QIP) despite the fact that, in present liquid state NMR experiments, no entanglement is found. We comment on how these experiments contribute to the future of QIP and include a brief discussion on the origin of the power of quantum computers.

Book Review:
On “Introduction to Quantum Computation and Information”
edited by Hoi-Kwong Lo, Sandu Popescu, and Tim Spiller  (pp177-168)
        D. Gottesman
QIC Webcorner:
Update (pp179-180)
        P. Kok

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