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. 

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References

SHOWING 1-10 OF 24 REFERENCES

Probabilistic and Statistical Aspects of Quantum Theory

Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV.

Quantum detection and estimation theory

  • H. Yuen
  • Physics
    Proceedings of the IEEE
  • 1978
TLDR
This online revelation quantum detection and estimation theory can be one of the options to accompany you in imitation of having other time.

States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin

States and effects.- Operations.- The first Representation theorem.- Composite systems.- The second representation theorem.- 6 Coexistent effects and observables.- References.

Maximum Entropy and Bayesian Methods.

Abstract : This volume contains selections from among the presentations at the Thirteenth International Workshop on Maximum Entropy and Bayesian Methods- MAXENT93 for short- held at the University of

Phys

  • Rev. 106, 620
  • 1957

Phys

  • Rev. 108, 171
  • 1957

Maximum entropy and bayesian methods in applied statistics

Phys

  • Rev. A 60, 3339
  • 1999

Phys

  • Rev. Lett. 80, 1571
  • 1998