A bstract In this paper, we introduce a new quantity called SVD entanglement entropy. This
is a generalization of entanglement entropy in that it depends on two different states, as in …

Bayes' rule, P (B| A) P (A)= P (A| B) P (B), is one of the simplest yet most profound,
ubiquitous, and far-reaching results of classical probability theory, with applications in any …

Categorical probability has recently seen significant advances through the formalism of
Markov categories, within which several classical theorems have been proven in entirely …

We study the positivity and causality axioms for Markov categories as properties of dilations
and information flow and also develop variations thereof for arbitrary semicartesian …

Markov categories are a novel framework to describe and treat problems in probability and
information theory. In this work we combine the categorical formalism with the traditional …

In 2017, D. Horsman, C. Heunen, M. Pusey, J. Barrett and R. Spekkens proved that there is
no physically reasonable assignment that takes a quantum channel and an initial state and …

In this work, we use the theory of quantum states over time to define an entropy $ S
(\rho,\mathcal {E}) $ associated with quantum processes $(\rho,\mathcal {E}) $, where $\rho …

Progress in psychology and the cognitive sciences is often taken to vindicate physicalism
and cast doubt on such extravagant metaphysical theses as dualism and idealism. The goal …

In statistical inference, retrodiction is the act of inferring potential causes in the past based
on knowledge of the effects in the present and the dynamics leading to the present …

We show that the essential properties of entropy (monotonicity, additivity and subadditivity)
are consequences of entropy being a monoidal natural transformation from the under …