# Quantum probabilities as Bayesian probabilities

@article{Caves2002QuantumPA, title={Quantum probabilities as Bayesian probabilities}, author={Carlton M. Caves and Christopher A. Fuchs and R. Schack}, journal={Physical Review A}, year={2002}, volume={65}, pages={022305} }

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the…

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## References

SHOWING 1-10 OF 23 REFERENCES

### Unknown Quantum States: The Quantum de Finetti Representation

- Mathematics
- 2001

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the…

### Quantum Foundations in the Light of Quantum Information

- Physics
- 2001

This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but…

### Quantum State Reconstruction From Incomplete Data

- Physics
- 1998

Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori…

### Quantum probability from decision theory?

- PhilosophyProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2000

In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical…

### Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

- Philosophy
- 1935

Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.

### Quantum Bayes rule

- Mathematics
- 2001

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…

### Quantum information: How much information in a state vector?

- Physics
- 1996

Quantum information refers to the distinctive information-processing properties of quantum systems, which arise when information is stored in or retrieved from nonorthogonal quantum states. More…

### Experimental test of nonlocal quantum correlation in relativistic configurations

- Physics
- 2001

We report on a new kind of experimental investigations of the tension between quantum nonlocally and relativity. Entangled photons are sent via an optical fiber network to two villages near Geneva,…

### Quantum Theory Needs No ‘Interpretation’

- Physics, Philosophy
- 2000

Purpose of this article is to stress the fact that Quantum Theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and…

### Promise of Bayesian Inference for Astrophysics

- Mathematics
- 1992

The "frequentist" approach to statistics, currently domi nating statistical practice in astrophysics, is compared to the historically older Bayesian approach, which is now growing in popularity in…