caa a22 4500 46790653X CHVBK 20180406152835.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10701-006-9057-9 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9057-9 Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix [Elektronische Daten] [Gui Long, Yi-Fan Zhou, Jia-Qi Jin, Yang Sun, Hai-Woong Lee] 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. Springer Science+Business Media, Inc., 2006 full density matrix nationallicence compressed density matrix nationallicence reduced density matrix nationallicence distinction of ensembles nationallicence Long Gui Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut Zhou Yi-Fan Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut Jin Jia-Qi Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut Sun Yang Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut Lee Hai-Woong Department of Physics, KAIST, 305-701, Dajeon, South Korea aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/8(2006-08-01), 1217-1243 0015-9018 36:8<1217 2006 36 10701 https://doi.org/10.1007/s10701-006-9057-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9057-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Long Gui Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut NATIONALLICENCE 700 1- Zhou Yi-Fan Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut NATIONALLICENCE 700 1- Jin Jia-Qi Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut NATIONALLICENCE 700 1- Sun Yang Department of Physics, Key Laboratory For Quantum Information and Measurements, Tsinghua University, 100084, Beijing, P.R China aut NATIONALLICENCE 700 1- Lee Hai-Woong Department of Physics, KAIST, 305-701, Dajeon, South Korea aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/8(2006-08-01), 1217-1243 0015-9018 36:8<1217 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer