×

zbMATH — the first resource for mathematics

A generalized statistical complexity measure: applications to quantum systems. (English) Zbl 1373.81116
Summary: A two-parameter family of complexity measures \(\tilde C(\alpha,\beta)\) based on the Rényi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz-Mancini-Calbet complexity, which is recovered for \(\alpha=1\) and \(\beta=2\). These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, \(\alpha\) or \(\beta\), goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator, and square well.
©2009 American Institute of Physics

MSC:
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A17 Measures of information, entropy
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Kolmogorov A. N., Probl. Inf. Transm. 1 pp 1– (1965)
[2] DOI: 10.1145/321356.321363 · Zbl 0158.25301 · doi:10.1145/321356.321363
[3] DOI: 10.1109/TIT.1976.1055501 · Zbl 0337.94013 · doi:10.1109/TIT.1976.1055501
[4] DOI: 10.1103/PhysRevLett.63.105 · doi:10.1103/PhysRevLett.63.105
[5] DOI: 10.1103/PhysRevA.32.2602 · doi:10.1103/PhysRevA.32.2602
[6] DOI: 10.1063/1.2121610 · doi:10.1063/1.2121610
[7] DOI: 10.1016/0375-9601(95)00867-5 · doi:10.1016/0375-9601(95)00867-5
[8] DOI: 10.1103/PhysRevE.66.011102 · doi:10.1103/PhysRevE.66.011102
[9] DOI: 10.1016/j.physleta.2008.06.012 · Zbl 1223.81175 · doi:10.1016/j.physleta.2008.06.012
[10] DOI: 10.1088/1751-8113/41/26/265303 · Zbl 1149.81398 · doi:10.1088/1751-8113/41/26/265303
[11] DOI: 10.1002/j.1538-7305.1948.tb00917.x · doi:10.1002/j.1538-7305.1948.tb00917.x
[12] DOI: 10.1002/j.1538-7305.1948.tb00917.x · doi:10.1002/j.1538-7305.1948.tb00917.x
[13] DOI: 10.1016/j.physa.2005.11.053 · doi:10.1016/j.physa.2005.11.053
[14] DOI: 10.1103/PhysRevA.46.3148 · doi:10.1103/PhysRevA.46.3148
[15] DOI: 10.1103/PhysRevE.68.026202 · doi:10.1103/PhysRevE.68.026202
[16] A. Rényi, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1: Contributions to the Theory of Statistics, 1961, p. 547.
[17] DOI: 10.1007/BF01016429 · Zbl 1082.82501 · doi:10.1007/BF01016429
[18] DOI: 10.1103/PhysRevA.55.1792 · doi:10.1103/PhysRevA.55.1792
[19] DOI: 10.1103/PhysRevA.59.1131 · doi:10.1103/PhysRevA.59.1131
[20] Romera E., Int. Rev. Phys. 3 pp 207– (2009)
[21] DOI: 10.1002/(SICI)1097-461X(1997)64:1<85::AID-QUA9>3.0.CO;2-Y · doi:10.1002/(SICI)1097-461X(1997)64:1<85::AID-QUA9>3.0.CO;2-Y
[22] DOI: 10.1016/j.bpc.2004.12.035 · doi:10.1016/j.bpc.2004.12.035
[23] Debnath L., Introduction to Hilbert Spaces with Applications (2005)
[24] DOI: 10.1007/978-3-642-84129-3 · doi:10.1007/978-3-642-84129-3
[25] DOI: 10.1007/978-1-4613-4104-8 · doi:10.1007/978-1-4613-4104-8
[26] Cohen-Tannoudji C., Quantum Mechanics (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.