SVD entanglement entropy
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 …
is a generalization of entanglement entropy in that it depends on two different states, as in …
From time-reversal symmetry to quantum Bayes' rules
AJ Parzygnat, J Fullwood - PRX Quantum, 2023 - APS
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 …
ubiquitous, and far-reaching results of classical probability theory, with applications in any …
Free gs-monoidal categories and free Markov categories
Categorical probability has recently seen significant advances through the formalism of
Markov categories, within which several classical theorems have been proven in entirely …
Markov categories, within which several classical theorems have been proven in entirely …
Dilations and information flow axioms in categorical probability
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 …
and information flow and also develop variations thereof for arbitrary semicartesian …
Markov categories and entropy
P Perrone - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
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 …
information theory. In this work we combine the categorical formalism with the traditional …
On quantum states over time
J Fullwood, AJ Parzygnat - Proceedings of the Royal …, 2022 - royalsocietypublishing.org
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 …
no physically reasonable assignment that takes a quantum channel and an initial state and …
On dynamical measures of quantum information
J Fullwood, AJ Parzygnat - arXiv preprint arXiv:2306.01831, 2023 - arxiv.org
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 …
(\rho,\mathcal {E}) $ associated with quantum processes $(\rho,\mathcal {E}) $, where $\rho …
The metaphysical neutrality of cognitive science
KC Chen, J Yoshimi - Synthese, 2023 - Springer
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 …
and cast doubt on such extravagant metaphysical theses as dualism and idealism. The goal …
Reversing information flow: retrodiction in semicartesian categories
AJ Parzygnat - arXiv preprint arXiv:2401.17447, 2024 - arxiv.org
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 …
on knowledge of the effects in the present and the dynamics leading to the present …
A Characterization of Entropy as a Universal Monoidal Natural Transformation
CT Li - arXiv preprint arXiv:2308.05742, 2023 - arxiv.org
We show that the essential properties of entropy (monotonicity, additivity and subadditivity)
are consequences of entropy being a monoidal natural transformation from the under …
are consequences of entropy being a monoidal natural transformation from the under …