We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies modified log-Sobolev inequality. In the discrete time setting, we channel strong data processing inequality with respect to its decoherence free part. Moreover, establish first general approximate tensorization property of relative entropy. This extends famous subadditivity entropy (SSA) ...

Abstract We classify discrete quantum subgroups in the double of $q$-deformation a compact semisimple Lie group, regarded as complexification. also record their classifications some variants groups. Along way, we show that doubles non-Kac-type groups do not admit analog lattices considered by Brannan–Chirvasitu–Viselter.

By using the decomposition of decoherence-free subalgebra N(T) in direct integrals factors, we obtain a structure theorem for every uniformly continuous quantum Markov semigroup. Moreover, prove that when there exists faithful normal invariant state, has to be atomic and decoherence takes place.

We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that in particular, one can construct a time evolution related to the logarithmic ...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

We address multi-parameter quantum estimation for one-dimensional discrete-time walks and its applications to metrology. use the walker as a probe unknown parameters encoded on coin degrees of freedom. find an analytic expression Fisher information matrix most general operator, show that only two out three can be accessed. also prove resulting two-parameter model is asymptotically classical i.e...

We model a quantum sensor network using techniques from state discrimination. The interaction between qubit detector and the environment is described by unitary operator, we will assume that at most one does interact. task to determine which or if none do. This involves choosing an initial of detectors measurement. consider global measurements in all are measured simultaneously. find entangled ...