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For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify bipartite state properties sufficient for the validity of a classical CHSH-form inequality and the perfect correlation form of the original Bell inequality for any bounded quantum observables. We also introduce a new general condition on a bipartite state and quantum...
We show that an effect tribe of fuzzy sets with the property that every is -measurable, where is the family of subsets of whose characteristic functions are central elements in , is a tribe. Moreover, a monotone -complete effect algebra with RDP with a Loomis-Sikorski representation , where the tribe has the property that every is -measurable, is a -MV-algebra.
This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.
In this paper we present an entropic description of quantum state obtained by interaction of one mode of quantized electromagnetic field with two two-level atoms inside a cavity, known as Tavis-Cumming model. Wehrl entropy has been calculated analytically and investigated as a function of the average value of the photon number operator. Husimi's Q function has been calculated and compared with the behaviour of the field entropy.
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