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Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of quantum systems, leading to the introduction of the quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.
The property of superadditivity of the quantum relative entropy states that, in a bipartite system $mathcal{H}_{AB}=mathcal{H}_A otimes mathcal{H}_B$, for every density operator $rho_{AB}$ one has $ D( rho_{AB} || sigma_A otimes sigma_B ) ge D( rho_A
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical reality--has em
We survey several problems related to logical aspects of quantum structures. In particular, we consider problems related to completions, decidability and axiomatizability, and embedding problems. The historical development is described, as well as recent progress and some suggested paths forward.
For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy S_{cond} as a function of measurement angle thetain[0,pi/2]. Numerical calculations show that the function S_{cond}(theta) for X states can hav
In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that every state ha