dorsal/arxiv
View SchemaDensity Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix
| Authors | Gui Lu Long, Yi-Fan Zhou, Jia-Qi Jin, Yang Sun, Hai-Woong Lee |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508207 |
| URL | https://arxiv.org/abs/quant-ph/0508207 |
| DOI | 10.1007/s10701-006-9057-9 |
| Journal | Foundations of Physics, 36 (8) 1217-1243 (2006) |
Abstract
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.
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"abstract": "We clarify different definitions of the density matrix by proposing the use\nof different names, the full density matrix for a single-closed quantum system,\nthe compressed density matrix for the averaged single molecule state from an\nensemble of molecules, and the reduced density matrix for a part of an\nentangled quantum system, respectively. We show that ensembles with the same\ncompressed density matrix can be physically distinguished by observing\nfluctuations of various observables. This is in contrast to a general belief\nthat ensembles with the same compressed density matrix are identical. Explicit\nexpression for the fluctuation of an observable in a specified ensemble is\ngiven. We have discussed the nature of nuclear magnetic resonance quantum\ncomputing. We show that the conclusion that there is no quantum entanglement in\nthe current nuclear magnetic resonance quantum computing experiment is based on\nthe unjustified belief that ensembles having the same compressed density matrix\nare identical physically. Related issues in quantum communication are also\ndiscussed.",
"arxiv_id": "quant-ph/0508207",
"authors": [
"Gui Lu Long",
"Yi-Fan Zhou",
"Jia-Qi Jin",
"Yang Sun",
"Hai-Woong Lee"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10701-006-9057-9",
"journal_ref": "Foundations of Physics, 36 (8) 1217-1243 (2006)",
"title": "Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix",
"url": "https://arxiv.org/abs/quant-ph/0508207"
},
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