scholarly journals Large Deviations at Level 2.5 for Markovian Open Quantum Systems: Quantum Jumps and Quantum State Diffusion

2021 ◽  
Vol 184 (1) ◽  
Author(s):  
Federico Carollo ◽  
Juan P. Garrahan ◽  
Robert L. Jack
Keyword(s):  
Quantum State ◽  
Large Time ◽  
Stochastic Dynamics ◽  
Large Deviation ◽  
Open Quantum Systems ◽  
Photon Detection ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Quantum Stochastic Processes ◽  
Large Time Limit

AbstractWe consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schrödinger equation and we discuss connections of these functionals to optimal control theory.

Primary state diffusion

1994 ◽  
Vol 447 (1929) ◽  
pp. 189-209 ◽  
Keyword(s):  
Quantum State ◽  
State Vector ◽  
Quantum Dynamics ◽  
Diffusion Theory ◽  
The State ◽  
Classical Dynamics ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Spontaneous Localization ◽  
Ordinary Quantum

Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Itô state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז 0 first determines the operator, to within an undetermined universal time constant ז 0 . The second and third conditions put opposing bounds on ז 0 . Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diósi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז 0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.

Quantum-state diffusion with adaptive noise

1998 ◽  
Vol 2 (2) ◽  
pp. 175-180 ◽  
Author(s):  
F.E. van Dorsselaer ◽  
G. Nienhuis
Keyword(s):  
Quantum State ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Adaptive Noise
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