Related papers: Complete entropic inequalities for quantum Markov …
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a…
We consider a generic modified logarithmic Sobolev inequality (mLSI) of the form $\mathrm{Ent}_{\mu}(e^f) \le \tfrac{\rho}{2} \mathbb{E}_\mu e^f \Gamma(f)^2$ for some difference operator $\Gamma$, and show how it implies two-level…
In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock-Varopoulos inequality in the…
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…
We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the…
Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields…
We establish an exact information-geometric inequality that remains valid regardless of the underlying dynamics, encompassing both Markovian and non-Markovian evolutions within the mixed-state domain. This inequality can be viewed as an…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
In the study of Markovian processes, one of the principal achievements is the equivalence between the $\Phi$-Sobolev inequalities and an exponential decrease of the $\Phi$-entropies. In this work, we develop a framework of Markov semigroups…
We present different characterizations of the notion of irreducibility for Quantum Markov Semigroups (QMSs) and investigate its relationship with other relevant features of the dynamics, such as primitivity, positivity improvement and…
We study finite-time spectral rigidity in reversible Markov chains via exact spectral relaxation dynamics. While the underlying identities follow classically from self-adjointness on $L^2(\pi)$, organizing the dynamics around the relaxation…
We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting…
The problem of finding good approximations of arbitrary 1-qubit gates is identical to that of finding a dense group generated by a universal subset of $SU(2)$ to approximate an arbitrary element of $SU(2)$. The Solovay-Kitaev Theorem is a…
We generalize the concepts of weak quantum logarithmic Sobolev inequality (LSI) and weak hypercontractivity (HC), introduced in the quantum setting by Olkiewicz and Zegarlinski, to the case of non-primitive quantum Markov semigroups (QMS).…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null…
We study the long time behavior of the stochastic quantization equation. Extending recent results by Mourrat and Weber we first establish a strong non-linear dissipative bound that gives control of moments of solutions at all positive times…
We prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to…
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the…