dorsal/arxiv
View SchemaHow `hot' are mixed quantum states?
| Authors | George Parfionov, Roman R. Zapatrin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606014 |
| URL | https://arxiv.org/abs/quant-ph/0606014 |
| DOI | 10.1142/S0219749907002803 |
| Journal | International Journal of Quantum Information (IJQI), Volume: 5, 311-317 (2007) |
Abstract
Given a mixed quantum state $\rho$ of a qudit, we consider any observable $M$ as a kind of `thermometer' in the following sense. Given a source which emits pure states with these or those distributions, we select such distributions that the appropriate average value of the observable $M$ is equal to the average Tr$M\rho$ of $M$ in the stare $\rho$. Among those distributions we find the most typical one, namely, having the highest differential entropy. We call this distribution conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter $\beta$. The expressions establishing the liaisons between the density operator $\rho$ and its temperature parameter $\beta$ are provided. Within this approach, the uniform mixed state has the highest `temperature', which tends to zero as the state in question approaches to a pure state.
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"abstract": "Given a mixed quantum state $\\rho$ of a qudit, we consider any observable $M$\nas a kind of `thermometer\u0027 in the following sense. Given a source which emits\npure states with these or those distributions, we select such distributions\nthat the appropriate average value of the observable $M$ is equal to the\naverage Tr$M\\rho$ of $M$ in the stare $\\rho$. Among those distributions we find\nthe most typical one, namely, having the highest differential entropy. We call\nthis distribution conditional Gibbs ensemble as it turns out to be a Gibbs\ndistribution characterized by a temperature-like parameter $\\beta$. The\nexpressions establishing the liaisons between the density operator $\\rho$ and\nits temperature parameter $\\beta$ are provided. Within this approach, the\nuniform mixed state has the highest `temperature\u0027, which tends to zero as the\nstate in question approaches to a pure state.",
"arxiv_id": "quant-ph/0606014",
"authors": [
"George Parfionov",
"Roman R. Zapatrin"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/S0219749907002803",
"journal_ref": "International Journal of Quantum Information (IJQI), Volume: 5,\n 311-317 (2007)",
"title": "How `hot\u0027 are mixed quantum states?",
"url": "https://arxiv.org/abs/quant-ph/0606014"
},
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