Interference in discrete Wigner functions

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.062315· OSTI ID:20976444

Cormick, Cecilia; Paz, Juan Pablo ^[1]

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1. Departamento de Fisica, FCEyN, UBA, Ciudad Universitaria Pabellon 1, 1428 Buenos Aires (Argentina)

We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider ''cat'' states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.

• OSTI ID: 20976444
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRECTIONS
ERRORS
FUNCTIONAL ANALYSIS
FUNCTIONS
HILBERT SPACE
INTERFERENCE
OSCILLATIONS
PHASE SPACE
QUANTUM COMPUTERS
QUANTUM MECHANICS
QUBITS
WIGNER THEORY