54 citations · 324 across the 30 of their papers we have counts for
18 papers · 1 filter
Causal confusion in quantum systems: distinguishing direct cause and common cause
Krisztina Tolotti, Riley Blank-Matthews, Arthur J. Parzygnat
The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we inves…
Quantum encodings that preserve persistent homology
Arthur J. Parzygnat, Andrew Vlasic
Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to…
Bipartite quantum states admitting a causal explanation
Minjeong Song, Arthur J. Parzygnat
The statistics of local measurements of joint quantum systems can sometimes be used to distinguish the spatiotemporal structure in which they were measured. We first prove that eve…
Towards structure-preserving quantum encodings
Arthur J. Parzygnat, Tai-Danae Bradley, Andrew Vlasic +1
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are c…
Quantum Mutual Information in Time
James Fullwood, Zhen Wu, Arthur J. Parzygnat +1
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present i…
Time-symmetric correlations for open quantum systems
Arthur J. Parzygnat, James Fullwood
Two-time expectation values of sequential measurements of dichotomic observables are known to be time symmetric for closed quantum systems. Namely, if a system evolves unitarily be…
Operator representation of spatiotemporal quantum correlations
James Fullwood, Arthur J. Parzygnat
While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, there does not exist an ana…
Virtual quantum broadcasting
Arthur J. Parzygnat, James Fullwood, Francesco Buscemi +1
The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we s…
On dynamical measures of quantum information
James Fullwood, Arthur J. Parzygnat
In this work, we use the theory of quantum states over time to define an entropy associated with quantum processes , where is a state and $\…
From time-reversal symmetry to quantum Bayes' rules
Arthur J. Parzygnat, James Fullwood
Bayes' rule is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theo…
Axioms for retrodiction: achieving time-reversal symmetry with a prior
Arthur J. Parzygnat, Francesco Buscemi
We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families…
On quantum states over time
James Fullwood, Arthur J. Parzygnat
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…
Towards a functorial description of quantum relative entropy
Arthur J. Parzygnat
A Bayesian functorial characterization of the classical relative entropy (KL divergence) of finite probabilities was recently obtained by Baez and Fritz. This was then generalized…
Conditional Distributions for Quantum Systems
Arthur J. Parzygnat
Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps ar…
A functorial characterization of von Neumann entropy
Arthur J. Parzygnat
Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving *-homomor…
A non-commutative Bayes' theorem
Arthur J. Parzygnat, Benjamin P. Russo
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $…
Inverses, disintegrations, and Bayesian inversion in quantum Markov categories
Arthur J. Parzygnat
We introduce quantum Markov categories as a structure that refines and extends a synthetic approach to probability theory and information theory so that it includes quantum probabi…
Non-commutative disintegrations: existence and uniqueness in finite dimensions
Arthur J. Parzygnat, Benjamin P. Russo
Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that…