Conditional Distributions for Quantum Systems
arXiv:2102.01529 · doi:10.4204/EPTCS.343.1
Abstract
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 are obtained via a categorical Bayesian inversion procedure. Simple criteria establishing when such linear maps are positive are obtained. Several examples are provided, including the standard EPR scenario, where the EPR correlations are reproduced in a purely compositional (categorical) manner. A comparison between the Bayes map, the Petz recovery map, and the Leifer-Spekkens acausal belief propagation is provided, illustrating some similarities and key differences.
arXiv commentIn Proceedings QPL 2021, arXiv:2109.04886
References in corpus (13)
- A survey of graphical languages for monoidal categories
- A generalized no-broadcasting theorem
- Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
- Disintegration and Bayesian Inversion via String Diagrams
- Quantum Dynamics as an analog of Conditional Probability
- Picturing classical and quantum Bayesian inference
- Anti- (Conjugate) Linearity
- From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality
- Quantum Probability and Quantum Information Theory
- A categorical foundation for Bayesian probability
- Lower and Upper Conditioning in Quantum Bayesian Theory