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Parity Measurements, Decoherence and Spiky Wigner Functions

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A. M. Ozorio de Almeida, O. Brodier

Quantum Physics · Submitted 10 Dec 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Even if $W(\x)$ resembles a classical distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$ and negative for $W_-$.

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arXiv IDquant-ph/0312098 (version 1)
Pith IDDR6AU7UH, Pith's permanent record of this paper and its review
CitationA. M. Ozorio de Almeida, O. Brodier. "Parity Measurements, Decoherence and Spiky Wigner Functions." arXiv:quant-ph/0312098 (2003). https://pith.science/paper/DR6AU7UH
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,557 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories . background 1.00 0.04 0.02 asserted 0.93
s1 Not so with the eigenvalues ($\pm 1$) of the parity operator. background 0.90 0.05 0.04 asserted 0.97
s2 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. interpretation 0.68 0.13 0.09 asserted 0.98
s3 The Wigner function should be a sensitive probe for this phenomenon, for it can be interpreted as the expectation value of the parity operator. background 0.52 0.09 0.07 hedged possibility 0.51
s4 We here derive the general form of Wigner functions $W_{\pm}$, resulting from an ideal parity measurement on $W(\x)$. contribution 0.94 0.94 0.10 asserted 1.00
s5 Even if $W(\x)$ resembles a classical distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$ and negative for $W_-$. result 0.99 0.78 0.29 asserted 0.98
s6 However we conjecture that $W_+$ always has negative values. result 0.47 0.38 0.30 speculative 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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