dorsal/arxiv
View SchemaParity Measurements, Decoherence and Spiky Wigner Functions
| Authors | A. M. Ozorio de Almeida, O. Brodier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312098 |
| URL | https://arxiv.org/abs/quant-ph/0312098 |
| DOI | 10.1088/0305-4470/37/24/L03 |
Abstract
Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories . Not so with the eigenvalues ($\pm 1$) of the parity operator. The effect of such a measurement on a mixture of even and odd states of the harmonic oscillator is akin to separating at a single stroke a pair of shuffled card decks: the result is a set of definite parity, though otherwise mixed. The Wigner function should be a sensitive probe for this phenomenon, for it can be interpreted as the expectation value of the parity operator. We here derive the general form of Wigner functions $W_{\pm}$, resulting from an ideal parity measurement on $W(\x)$. Even if $W(\x)$ resembles a classical distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$ and negative for $W_-$. However we conjecture that $W_+$ always has negative values.
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"abstract": "Notwithstanding radical conceptual differences between classical and quantum\nmechanics, it is usually assumed that physical measurements concern observables\ncommon to both theories . Not so with the eigenvalues ($\\pm 1$) of the parity\noperator. The effect of such a measurement on a mixture of even and odd states\nof the harmonic oscillator is akin to separating at a single stroke a pair of\nshuffled card decks: the result is a set of definite parity, though otherwise\nmixed. The Wigner function should be a sensitive probe for this phenomenon, for\nit can be interpreted as the expectation value of the parity operator. We here\nderive the general form of Wigner functions $W_{\\pm}$, resulting from an ideal\nparity measurement on $W(\\x)$. Even if $W(\\x)$ resembles a classical\ndistribution, $W_{\\pm}$ displays a quantum spike, which is positive for $W_+$\nand negative for $W_-$. However we conjecture that $W_+$ always has negative\nvalues.",
"arxiv_id": "quant-ph/0312098",
"authors": [
"A. M. Ozorio de Almeida",
"O. Brodier"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/24/L03",
"title": "Parity Measurements, Decoherence and Spiky Wigner Functions",
"url": "https://arxiv.org/abs/quant-ph/0312098"
},
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