54 citations · 324 across the 30 of their papers we have counts for
31 papers
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…
Bayesian inference and retrodiction for faithful states on von Neumann algebras
Pradyut Karmakar, Arthur J. Parzygnat
Retrodiction is the act of inferring a cause from its effects, the most common example of which is Bayesian inference. Retrodiction can be defined by its structural process-theoret…
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…
When can phonon modes be trapped by arbitrarily weak local defects? Rigorous sufficient conditions in a monatomic lattice
Jaden Thomas-Markarian, Jaden Thomas, Rodrigo Arrieta +3
Although many studies have shown that localized defects in vibrational lattices can trap localized phonon modes for particular geometries, there has been no general proof of locali…
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…
Reversing information flow: retrodiction in semicartesian categories
Arthur J. Parzygnat
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…
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 $\…
SVD Entanglement Entropy
Arthur J. Parzygnat, Tadashi Takayanagi, Yusuke Taki +1
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 pre-…
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…
Bayesian inversion and the Tomita-Takesaki modular group
Luca Giorgetti, Arthur J. Parzygnat, Alessio Ranallo +1
We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the ex…
The information loss of a stochastic map
James Fullwood, Arthur J. Parzygnat
We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the condi…
Noncommutative Differential K-theory
Byungdo Park, Arthur J. Parzygnat, Corbett Redden +1
We introduce a differential extension of algebraic K-theory of an algebra using Karoubi's Chern character. In doing so, we develop a necessary theory of secondary transgression for…
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…