Spin coherent states, Bell states, spin Hamilton operators, entanglement, Husimi distribution, uncertainty relation and Bell inequality

We investigate spin Hamilton operators and compare spin coherent states and Bell states concerning entanglement, Husimi distributions, uncertainty relation and Bell inequality. The distances between spin coherent states and Bell states are derived. The Rayleigh quotients of spin Hamilton operators for spin coherent states and Bell states are evaluated and compared.

Coherent representation of fields and deformation quantization

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

ENTROPY CREATION IN RELATIVISTIC HEAVY ION COLLISIONS

We review current ideas on entropy production during the different stages of a relativistic nuclear collision. This includes recent results on decoherence entropy and the entropy produced during the hydrodynamic phase by viscous effects. We start by a discussion of decoherence caused by gluon bremsstrahlung in the very first interactions of gluons from the colliding nuclei. We then present a general framework, based on the Husimi distribution function, for the calculation of entropy growth in quantum field theories, which is applicable to the early ("glasma") phase of the collision during which most of the entropy is generated. The entropy calculated from the Husimi distribution exhibits linear growth when the quantum field contains unstable modes and the growth rate is asymptotically equal to the Kolmogorov–Sinaï entropy. We outline how the approach can be used to investigate the problem of entropy production in a relativistic heavy ion reaction from first principles. We show that the same result can be obtained in the framework of a completely different approach called eigenstate thermalization hypothesis. Finally we discuss some recent results on entropy production in the strong coupling limit, as obtained from AdS/CFT duality.