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Journal of Mathematical Physics / Volume 49 / Issue 8 / QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)

J. Math. Phys. 49, 082103 (2008); doi:10.1063/1.2966133 (13 pages)

On the epistemic view of quantum states

Michael Skotiniotis, Aidan Roy, and Barry C. Sanders

Institute for Quantum Information Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2l 1N1, Canada

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(Received 4 July 2007; accepted 11 July 2008; published online 18 August 2008)

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens’ toy model. We then test whether these axioms can be extended to capture more quantum phenomena by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens’ toy model cannot produce an equivalence with the Clifford group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE STM AND QUANTUM THEORY
  3. RELAXING THE STM
  4. DISCUSSION

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KEYWORDS and PACS

Keywords

group theory, quantum theory

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ARTICLE DATA

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http://link.aip.org/link/doi/10.1063/1.2966133

PUBLICATION DATA

ISSN:

0022-2488 (print)  
1089-7658 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    R. W. Spekkens, Phys. Rev. A 75, 032110 (2007).

    S. Weinberg, Phys. Rev. Lett. 62, 485 (1989).

    A. Peres, Phys. Rev. Lett. 63, 1114 (1989).

    D. M. Appleby, J. Math. Phys. 46, 052107 (2005)JMAPAQ000046000005052107000001.


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