Quantum probabilities of composite events in quantum measurements with multimode states
arXiv:1308.5604 · doi:10.1088/1054-660X/23/10/105502
Abstract
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that the Luders 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 weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for the mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. A special attention is payed to the application of the approach to systems with multimode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes.
Latex file, 28 pages, no figures
References in corpus (10)
- Quantum channels and their entropic characteristics
- Quantum Graphical Models and Belief Propagation
- Quantum theory of successive projective measurements
- Effects of symmetry breaking in finite quantum systems
- Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
- Quantum Dynamics as an analog of Conditional Probability
- Resonance Theory of Decoherence and Thermalization
- Quantum decision theory as quantum theory of measurement
- Dynamics of Collective Decoherence and Thermalization
- The Collapse of Bell Determinism