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

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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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Authors and Affiliations

  1. Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, Beijing, 100084, P.R China

    Gui Lu Long, Yi-Fan Zhou, Jia-Qi Jin & Yang Sun

  2. Key Laboratory for Atomic and Molecular NanoSciences, Tsinghua University, Beijing, 100084, P.R China

    Gui Lu Long

  3. Department of Physics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Yang Sun

  4. Department of Physics, KAIST, Dajeon, 305-701, South Korea

    Hai-Woong Lee

Authors
  1. Gui Lu Long
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  2. Yi-Fan Zhou
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  3. Jia-Qi Jin
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  4. Yang Sun
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  5. Hai-Woong Lee
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Correspondence to Gui Lu Long.

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Long, G.L., Zhou, YF., Jin, JQ. et al. Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix. Found Phys 36, 1217–1243 (2006). https://doi.org/10.1007/s10701-006-9057-9

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  • DOI: https://doi.org/10.1007/s10701-006-9057-9

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