Correlation properties of entangled multiphoton states and Bernstein’s paradox
A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein’s paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.
KeywordsEntangle State Cluster State Qubit State Polarization Beam Splitter Mixed Moment
Unable to display preview. Download preview PDF.
- 2.G. S. Greenstein and A. G. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (Jones and Bartlett, London, 2005; Intellekt, Moscow, 2008).Google Scholar
- 3.J. Preskill, Quantum Information and Computation (California Institute of Technology, Pasadena, California, United States, 1998; Institute of Computer Science, Moscow, 2008).Google Scholar
- 4.Quantum Imaging, Ed. by M. I. Kolobov (Springer-Verlag, Berlin, 2006; Fizmatlit, Moscow, 2009).Google Scholar
- 15.K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, arXiv:quant-ph1112.6238v1.Google Scholar
- 17.A. V. Belinskii and D. N. Klyshko, JETP 75(4), 606 (1994).Google Scholar
- 22.A. N. Malakhov, Cumulant Analysis of Random Non-Gaussian Processes and Their Transformations (Sovetskoe Radio, Moscow, 1978) [in Russian].Google Scholar
- 23.S. A. Akhmanov, Yu. E. D’yakov, and A. S. Chirkin, Statistical Radiophysics and Optics: Random Vibrations and Waves in Linear Systems (Fizmatlit, Moscow, 2010) [in Russian].Google Scholar
- 25.I. S. Zhukova, G. A. Malinovskaya, and A. I. Saichev, Modern Methods of Analysis of Random Processes and Fields (Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia, 2006) [in Russian].Google Scholar