# Quantum causality, stochastics, trajectories and information

@article{Belavkin2002QuantumCS, title={Quantum causality, stochastics, trajectories and information}, author={Viacheslav P. Belavkin}, journal={Reports on Progress in Physics}, year={2002}, volume={65}, pages={353-420} }

A history of the discovery of `new' quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information. Modern quantum theory, which has been developed during the last 20 years for the treatment of quantum open systems including quantum noise, decoherence, quantum diffusions and spontaneous jumps occurring under continuous in time observation, is not yet a part of the standard curriculum of quantum…

## 22 Citations

Quantum Trajectories, State Diffusion, and Time-Asymmetric Eventum Mechanics

- Physics
- 2003

We show that the quantum stochastic Langevin model for continuous in time measurements provides an exact formulation of the von Neumann uncertainty error-disturbance principle. Moreover, as it was…

ON THE DYNAMICAL SOLUTION OF QUANTUM MEASUREMENT PROBLEM

- Physics
- 2003

The development of quantum measurement theory, initiated by von Neumann, only indicated a possibility for resolution of the interpreta- tional crisis of quantum mechanics. We do this by divorcing the…

Mixing quantum and classical mechanics and uniqueness of Planck's constant

- Physics, Mathematics
- 2003

Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras (HAs), respectively (Grgin and Petersen 1974 J. Math. Phys. 15 764, Sahoo 1977 Pramana 8…

Extended statistical modeling under symmetry; the link toward quantum mechanics

- Mathematics, Physics
- 2006

We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set A of incompatible experiments, and a…

Quantum Dynamics, Minkowski-Hilbert space, and A Quantum Stochastic Duhamel Principle

- PhysicsArXiv
- 2014

A beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be `unraveled' in a second-quantized Minkowski space is presented.

Entangled States and Quantum Causality Threshold in the General Theory of Relativity

- Physics
- 2005

This article shows, Synge-Weber's classical problem statement about two particles interacting by a signal can be reduced to the case where the same particle is located in two different points A and B…

On Quantum Statistical Inference, II

- Physics
- 2003

Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for…

Heisenberg evolution of quantum observables represented by unbounded operators

- Mathematics, Physics
- 2008

Viacheslav Pavlovich Belavkin, 1946-2012: In Memory of Professor V. P. Belavkin

- PhysicsOpen Syst. Inf. Dyn.
- 2013

A number of remarkable and highly original results in mathematical physics and quantum probability are obtained, and there are theorems and equations named after him, including the Belavkin quantum filtering equation — the evolution equation for observed quantum systems.

## References

SHOWING 1-10 OF 102 REFERENCES

Event enhanced quantum theory and piecewise deterministic dynamics

- Physics
- 1995

The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise…

A stochastic Hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories

- Physics
- 1996

We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that…

Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics

- Mathematics
- 1985

The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how…

Nondemolition principle of quantum measurement theory

- Physics
- 1994

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the…

Reduction of a wave packet in quantum Brownian motion.

- PhysicsPhysical review. D, Particles and fields
- 1989

In an open quantum system, dissipation can cause decorrelation on a time scale significantly shorter than the relaxation time which characterizes the approach of the system to thermodynamic equilibrium, and it is demonstrated that the density matrix decays rapidly toward a mixture of ``approximate eigenstates'' of the ``pointer observable,'' which commutes with the system-environment interaction Hamiltonian.

"Relative State" Formulation of Quantum Mechanics

- Physics
- 1957

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as…

Measurements continuous in time and a posteriori states in quantum mechanics

- Physics
- 1991

Measurements continuous in time have been consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been…

Continuous Quantum Measurement:. Local and Global Approaches

- Physics
- 1997

In 1979 B. Menski suggested a formula for the linear propagator of a quantum system with continuously observed position in terms of a heuristic Feynman path integral. In 1989 the aposterior linear…

Quantum continual measurements and a posteriori collapse on CCR

- Physics
- 1992

A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior…