dorsal/arxiv
View SchemaStability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements
| Authors | Akira Shimizu, Takayuki Miyadera |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203106 |
| URL | https://arxiv.org/abs/quant-ph/0203106 |
| DOI | 10.1103/PhysRevLett.89.270403 |
| Journal | Phys.Rev.Lett.89:270403,2002 |
Abstract
We study the stability of quantum states of macroscopic systems of finite volume V, against weak classical noises (WCNs), weak perturbations from environments (WPEs), and local measurements (LMs). We say that a pure state is `fragile' if its decoherence rate is anomalously great, and `stable against LMs' if the result of a LM is not affected by another LM at a distant point. By making full use of the locality and huge degrees of freedom, we show the following: (i) If square fluctuation of every additive operator is O(V) or less for a pure state, then it is not fragile in any WCNs or WPEs. (ii) If square fluctuations of some additive operators are O(V^2) for a pure state, then it is fragile in some WCNs or WPEs. (iii) If a state (pure or mixed) has the `cluster property,' then it is stable against LMs, and vice versa. These results have many applications, among which we discuss the mechanism of symmetry breaking in finite systems.
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"abstract": "We study the stability of quantum states of macroscopic systems of finite\nvolume V, against weak classical noises (WCNs), weak perturbations from\nenvironments (WPEs), and local measurements (LMs). We say that a pure state is\n`fragile\u0027 if its decoherence rate is anomalously great, and `stable against\nLMs\u0027 if the result of a LM is not affected by another LM at a distant point. By\nmaking full use of the locality and huge degrees of freedom, we show the\nfollowing: (i) If square fluctuation of every additive operator is O(V) or less\nfor a pure state, then it is not fragile in any WCNs or WPEs. (ii) If square\nfluctuations of some additive operators are O(V^2) for a pure state, then it is\nfragile in some WCNs or WPEs. (iii) If a state (pure or mixed) has the `cluster\nproperty,\u0027 then it is stable against LMs, and vice versa. These results have\nmany applications, among which we discuss the mechanism of symmetry breaking in\nfinite systems.",
"arxiv_id": "quant-ph/0203106",
"authors": [
"Akira Shimizu",
"Takayuki Miyadera"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th"
],
"doi": "10.1103/PhysRevLett.89.270403",
"journal_ref": "Phys.Rev.Lett.89:270403,2002",
"title": "Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements",
"url": "https://arxiv.org/abs/quant-ph/0203106"
},
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