# Quantum Bayes rule

@article{Schack2001QuantumBR, title={Quantum Bayes rule}, author={R. Schack and Todd A. Brun and Carlton M. Caves}, journal={Physical Review A}, year={2001}, volume={64}, pages={014305} }

We state a quantum version of Bayes’s rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.

## 111 Citations

Quantum Bayesian Statistical Inference

- Mathematics, Computer Science
- 2022

A quantum analogue of Bayes rule is put forward, which states how a prior normal state of a quantum system updates under those observations, and the fundamental notions and results of Bayesian statistics are generalized according to the quantumBayes rule.

Bayes + Hilbert = Quantum Mechanics

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We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality…

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- PhysicsArXiv
- 2014

We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Luders’ rules, is a special case of the constrained maximisation of a quantum relative…

2 Bayes – Laplace and Jeffrey ’ s rules as entropic projections

- Physics
- 2018

We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Lüders’ rules, is a special case of the constrained maximisation of a quantum relative…

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- Physics
- 2008

In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy…

Quantum-Bayesian Coherence

- Philosophy
- 2009

It is argued that the Born Rule should be seen as an empirical addition to Bayesian reasoning itself, and how to view it as a normative rule in addition to usual Dutch-book coherence is shown.

Quantum estimation via the minimum Kullback entropy principle

- Computer Science
- 2007

The resulting minimum Kullback entropy principle is exploited for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and applies it as a tool forThe estimation of weak Hamiltonian processes.

Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

- Physics
- 2016

We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality…

Inferring the Gibbs state of a small quantum system

- Computer Science
- 2011

This work shows how the two issues can be tackled with the help of Bayesian model selection and Bayesian interpolation, respectively, and illustrates the use of these Bayesian techniques with a number of simple examples.

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