# Quantum probabilities of composite events in quantum measurements with multimode states

@article{Yukalov2013QuantumPO, title={Quantum probabilities of composite events in quantum measurements with multimode states}, author={Vyacheslav I. Yukalov and Didier Sornette}, journal={Laser Physics}, year={2013}, volume={23} }

The problem of defining quantum probabilities of composite events is considered. This problem is of great importance for the theory of quantum measurements and for quantum decision theory, which is a part of measurement theory. We show that the Lüders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a…

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## References

SHOWING 1-10 OF 110 REFERENCES

### Quantum probabilities as Bayesian probabilities

- Philosophy
- 2002

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,…

### A Quantum-Bayesian Route to Quantum-State Space

- Physics
- 2011

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…

### Quantum theory of successive projective measurements

- Physics
- 2007

We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in…

### Quantum dynamics as an analog of conditional probability (12 pages)

- Mathematics
- 2006

Quantum theory can be regarded as a noncommutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional…

### Composite systems and the role of the complex numbers in quantum mechanics

- Mathematics, Physics
- 2004

An axiomatic approach to the mathematical formalism of quantum mechanics, based upon a certain concept of conditional probability, has been proposed in two recent papers by the author. It leads to…

### Quantum channels and their entropic characteristics

- Computer Science, PhysicsReports on progress in physics. Physical Society
- 2012

A survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems, and the remarkable role of specific quantum correlations—entanglement—as a novel communication resource is stressed.

### Quantum dynamics in open quantum-classical systems

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2015

This review discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum- classical Liouville dynamics, as well as methods for simulating the dynamics.

### An Approach to Quantum Mechanics via Conditional Probabilities

- Mathematics
- 2008

Abstract
The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new…

### Processing Information in Quantum Decision Theory

- Computer ScienceEntropy
- 2009

Conditional maximization of entropy, equivalent to the minimization of an information functional, makes it possible to connect the quantum and classical decision theories, showing that the latter is the limit of the former under vanishing interference terms.