Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

Details Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

2005-08-27

arxiv.org/abs/quant-ph/0508207v2

Foundations of Physics, 36 (8) 1217-1243 (2006)

Physics

Quantum Physics

26 pages. To appear in Foundations of Physics, 36 (8), 2006

Scientific paper

10.1007/s10701-006-9057-9

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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