Dressed coherent states in finite quantum systems: a cooperative game theory approach

Abstract

A quantum system with variables in Z(d) is considered. Coherent density matrices and coherent projectors of rank n are introduced, and their properties (e.g., the resolution of the identity) are dis- cussed. Cooperative game theory and in particular the Shapley methodology, is used to renormalize coherent states, into a particular type of coherent density matrices (dressed coherent states). The Q-function of a Hermitian operator, is then renormalized into a physical analogue of the Shapley values. Both the Q-function and the Shapley values, are used to study the relocation of a Hamilto- nian in phase space as the coupling constant varies, and its effect on the ground state of the system. The formalism is also generalized for any total set of states, for which we have no resolution of the identity. The dressing formalism leads to density matrices that resolve the identity, and makes them practically useful.

References in corpus (6)

• On mutually unbiased bases
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Husimi distribution and phase space analysis of Dicke model quantum phase transition
• Analytic Representation of Finite Quantum Systems
• Mobius operators and non-additive quantum probabilities in the Birkhoff-von Neumann lattice
• Comonotonicity and Choquet integrals of Hermitian operators and their applications

Cited by in corpus (3)

• Renormalization of total sets of states into generalized bases with a resolution of the identity
• Equivalence classes of coherent projectors in a Hilbert space with prime dimension: Q functions and their Gini index
• Random projectors with continuous resolutions of the identity in a finite-dimensional Hilbert space