dorsal/arxiv
View SchemaSome Features of the Conditional $q$-Entropies of Composite Quantum Systems
| Authors | J. Batle, A. R. Plastino, M. Casas, A. Plastino |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306188 |
| URL | https://arxiv.org/abs/quant-ph/0306188 |
| DOI | 10.1140/epjb/e2003-00291-3 |
| Journal | European Physical Journal B 35, 391 (2003) |
Abstract
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$ through the quantity $\omega_q = Tr\rho^q$, and admit as a particular instance the standard von Neumann entropy in the limit case $q\to 1$. A comprehensive numerical survey of the space of pure and mixed states of bipartite systems is here performed, in order to determine the volumes in state space occupied by those states exhibiting various special properties related to the signs of their conditional $q$-entropies and to their connections with other separability-related features, including the majorization condition. Different values of the entropic parameter $q$ are considered, as well as different values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces associated with the constituting subsystems. Special emphasis is paid to the analysis of the monotonicity properties, both as a function of $q$ and as a function of $N_1$ and $N_2$, of the various entropic functionals considered.
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"abstract": "The study of conditional $q$-entropies in composite quantum systems has\nrecently been the focus of considerable interest, particularly in connection\nwith the problem of separability. The $q$-entropies depend on the density\nmatrix $\\rho$ through the quantity $\\omega_q = Tr\\rho^q$, and admit as a\nparticular instance the standard von Neumann entropy in the limit case $q\\to\n1$. A comprehensive numerical survey of the space of pure and mixed states of\nbipartite systems is here performed, in order to determine the volumes in state\nspace occupied by those states exhibiting various special properties related to\nthe signs of their conditional $q$-entropies and to their connections with\nother separability-related features, including the majorization condition.\nDifferent values of the entropic parameter $q$ are considered, as well as\ndifferent values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces\nassociated with the constituting subsystems. Special emphasis is paid to the\nanalysis of the monotonicity properties, both as a function of $q$ and as a\nfunction of $N_1$ and $N_2$, of the various entropic functionals considered.",
"arxiv_id": "quant-ph/0306188",
"authors": [
"J. Batle",
"A. R. Plastino",
"M. Casas",
"A. Plastino"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjb/e2003-00291-3",
"journal_ref": "European Physical Journal B 35, 391 (2003)",
"title": "Some Features of the Conditional $q$-Entropies of Composite Quantum Systems",
"url": "https://arxiv.org/abs/quant-ph/0306188"
},
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