dorsal/arxiv
View SchemaInterference in discrete Wigner functions
| Authors | Cecilia Cormick, Juan Pablo Paz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608200 |
| URL | https://arxiv.org/abs/quant-ph/0608200 |
| DOI | 10.1103/PhysRevA.74.062315 |
| Journal | Phys. Rev. A 74, 062315 (2006) (9 pages) |
Abstract
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. 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 analysing the phase-space representation of the five-qubit error-correcting code.
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"abstract": "We analyse some features of the class of discrete Wigner functions that was\nrecently introduced by Gibbons et al. to represent quantum states of systems\nwith power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101\n(2004)]. We consider \"cat\" states obtained as coherent superpositions of states\nwith positive Wigner function; for such states we show that the oscillations of\nthe discrete Wigner function typically spread over the entire discrete\nphase-space (including the regions where the two interfering states are\nlocalized). This is a generic property which is in sharp contrast with the\nusual attributes of Wigner functions that make them useful candidates to\ndisplay the existence of quantum coherence through oscillations. However, it is\npossible to find subsets of cat states with a natural phase-space\nrepresentation, in which the oscillatory regions remain localized. We show that\nthis can be done for interesting families of stabilizer states used in quantum\nerror-correcting codes, and illustrate this by analysing the phase-space\nrepresentation of the five-qubit error-correcting code.",
"arxiv_id": "quant-ph/0608200",
"authors": [
"Cecilia Cormick",
"Juan Pablo Paz"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.062315",
"journal_ref": "Phys. Rev. A 74, 062315 (2006) (9 pages)",
"title": "Interference in discrete Wigner functions",
"url": "https://arxiv.org/abs/quant-ph/0608200"
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