dorsal/arxiv
View SchemaNonclassicality in Weak Measurements
| Authors | Lars M. Johansen, Alfredo Luis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408038 |
| URL | https://arxiv.org/abs/quant-ph/0408038 |
| DOI | 10.1103/PhysRevA.70.052115 |
| Journal | Phys. Rev. A 70 (2004) 052115 |
Abstract
We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation value over an infinite class of different generalized Kirkwood quasi-probability distributions. "Strange" weak values for which the real part exceeds the eigenvalue spectrum of the observable can only be found if the Terletsky-Margenau-Hill distribution is negative, or, equivalently, if the real part of the weak value of the density operator is negative. We find that a classical model of a weak measurement exists whenever the Terletsky-Margenau-Hill representation of the observable equals the classical representation of the observable and the Terletsky-Margenau-Hill distribution is nonnegative. Strange weak values alone are not sufficient to obtain a contradiction with classical models. We propose feasible weak measurements of photon number of the radiation field. Negative weak values of energy contradicts all classical stochastic models, whereas negative weak values of photon number contradict all classical stochastic models where the energy is bounded from below by the zero-point energy. We examine coherent states in particular, and find negative weak values with probabilities of 16% for kinetic energy (or squared field quadrature), 8% for harmonic oscillator energy and 50% for photon number. These experiments are robust against detector inefficiency and thermal noise.
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"abstract": "We examine weak measurements of arbitrary observables where the object is\nprepared in a mixed state and on which measurements with imperfect detectors\nare made. The weak value of an observable can be expressed as a conditional\nexpectation value over an infinite class of different generalized Kirkwood\nquasi-probability distributions. \"Strange\" weak values for which the real part\nexceeds the eigenvalue spectrum of the observable can only be found if the\nTerletsky-Margenau-Hill distribution is negative, or, equivalently, if the real\npart of the weak value of the density operator is negative. We find that a\nclassical model of a weak measurement exists whenever the\nTerletsky-Margenau-Hill representation of the observable equals the classical\nrepresentation of the observable and the Terletsky-Margenau-Hill distribution\nis nonnegative. Strange weak values alone are not sufficient to obtain a\ncontradiction with classical models.\n We propose feasible weak measurements of photon number of the radiation\nfield. Negative weak values of energy contradicts all classical stochastic\nmodels, whereas negative weak values of photon number contradict all classical\nstochastic models where the energy is bounded from below by the zero-point\nenergy. We examine coherent states in particular, and find negative weak values\nwith probabilities of 16% for kinetic energy (or squared field quadrature), 8%\nfor harmonic oscillator energy and 50% for photon number. These experiments are\nrobust against detector inefficiency and thermal noise.",
"arxiv_id": "quant-ph/0408038",
"authors": [
"Lars M. Johansen",
"Alfredo Luis"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.052115",
"journal_ref": "Phys. Rev. A 70 (2004) 052115",
"title": "Nonclassicality in Weak Measurements",
"url": "https://arxiv.org/abs/quant-ph/0408038"
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