Qubit phase space: SU(n) coherent-state P representations

Barry, D. W. and Drummond, P. D. (2008) Qubit phase space: SU(n) coherent-state P representations. Physical Review A, 78 5: 052108 -1-052108 -13. doi:10.1103/PhysRevA.78.052108

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Author Barry, D. W.
Drummond, P. D.
Title Qubit phase space: SU(n) coherent-state P representations
Formatted title
Qubit phase space: SU(n) coherent-state P representations
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2008-11
Sub-type Article (original research)
DOI 10.1103/PhysRevA.78.052108
Open Access Status File (Publisher version)
Volume 78
Issue 5
Start page 052108 -1
End page 052108 -13
Total pages 13
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
We introduce a phase-space representation for qubits and spin models. The technique uses an SU (n) coherent-state basis and can equally be used for either static or dynamical simulations. We review previously known definitions and operator identities, and show how these can be used to define an off-diagonal, positive phase-space representation analogous to the positive- P function. As an illustration of the phase-space method, we use the example of the Ising model, which has exact solutions for the finite-temperature canonical ensemble in two dimensions. We show how a canonical ensemble for an Ising model of arbitrary structure can be efficiently simulated using SU(2) or atomic coherent states. The technique utilizes a transformation from a canonical (imaginary-time) weighted simulation to an equivalent unweighted real-time simulation. The results are compared to the exactly soluble two-dimensional case. We note that Ising models in one, two, or three dimensions are potentially achievable experimentally as a lattice gas of ultracold atoms in optical lattices. The technique is not restricted to canonical ensembles or to Ising-like couplings. It is also able to be used for real-time evolution and for systems whose time evolution follows a master equation describing decoherence and coupling to external reservoirs. The case of SU (n) phase space is used to describe n -level systems. In general, the requirement that time evolution be stochastic corresponds to a restriction to Hamiltonians and master equations that are quadratic in the group generators or generalized spin operators.
Keyword Cluster Monte-Carlo
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 9 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 03 Sep 2009, 09:13:38 EST by Mr Andrew Martlew on behalf of ARC Centre of Excellence for Quantum-Atom Optics