Related papers: A necessary and sufficient condition for a matrix …
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of…
Let $A$ be a self-adjoint operator acting over a space $X$ endowed with a partition. We give lower bounds on the energy of a mixed state $\rho$ from its distribution in the partition and the spectral density of $A$. These bounds improve…
A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
The notion of $\Delta$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $\Delta$-weakly mixing sets is…
In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states:…
We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is…
Given a non-empty closed convex subset $\mathsf{F}$ of density matrices, we formulate conditions that guarantee the existence of an $\mathsf{F}$-morphism (namely, a completely positive trace-preserving linear map that maps $\mathsf{F}$ into…
Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
The search for possible mixing patterns of charged leptons and neutrinos is important to get clues of the origin of nearly maximal mixings, since there are some preferred bases of the lepton mass matrices given by underlying theories. We…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…
We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is shown that every ergodic invariant measure (finite or…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We establish the existence and finiteness of equilibrium states for a class of partially hyperbolic endomorphisms. In our first result, we assume that the central direction is simple. In the second result, we consider the case where there…
Mixing for measure-preserving group actions is a fundamental notion in ergodic theory, with different phenomena arising for different acting groups. In 1993, Klaus Schmidt and Tom Ward proved that 2-mixing implies mixing of all orders for…
The extension of thermodynamic principles to active matter remains a challenge due to the non-equilibrium nature inherent to active systems. In this study, we introduce a framework to assess entropy in our minimal macroscopic experiment…