# 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.

## 114 Citations

### Quantum Bayesian Statistical Inference

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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.

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In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of…

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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…

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- 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…

### Reasoning about quantum systems at the macroscopic level

- 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

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- 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.

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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
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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…

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