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The Choquet integral as an approximation to density matrices with incomplete informationVourdas, Apostolos 18 March 2022 (has links)
yes / Highlights:
Non-additive probabilities and Choquet integrals in a classical context.
The use of Choquet integrals in a quantum context.
Approximation of partially known density matrices with Choquet integrals.
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Comonotonicity and Choquet integrals of Hermitian operators and their applications.Vourdas, Apostolos 20 January 2016 (has links)
yes / In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive
semide nite operator , is de ned in terms of the d2 coherent states in this system. The Choquet
integral CQ( ) of the Q-function of , is introduced using a ranking of the values of the Q-function,
and M obius transforms which remove the overlaps between coherent states. It is a gure of merit
of the quantum properties of Hermitian operators, and it provides upper and lower bounds to
various physical quantities in terms of the Q-function. Comonotonicity is an important concept
in the formalism, which is used to formalize the vague concept of physically similar operators.
Comonotonic operators are shown to be bounded, with respect to an order based on Choquet
integrals. Applications of the formalism to the study of the ground state of a physical system, are
discussed. Bounds for partition functions, are also derived.
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