3 research outputs found
Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix
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.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200