Interference of Quantum Trajectories
- URL: http://arxiv.org/abs/2102.10355v2
- Date: Fri, 7 Jan 2022 14:41:07 GMT
- Title: Interference of Quantum Trajectories
- Authors: Brecht Donvil, and Paolo Muratore-Ginanneschi
- Abstract summary: We prove that general time-local quantum master equations admit an unraveling described by ordinary jump-stochastic differential equations.
The influence martingale satisfies a $ 1d $ differential equation enslaved to the ones governing the quantum trajectories.
Our result proves the existence of a Markovian quantum trajectory picture in the Hilbert space of the system.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We extend quantum trajectory theory to encompass the evolution of a large
class of open quantum systems interacting with an environment at {arbitrary
coupling strength}. Specifically, we prove that general time-local quantum
master equations admit an unraveling described by ordinary jump-stochastic
differential equations. The sufficient condition is to weigh the state vector
Monte Carlo averages by a probability pseudo-measure which we call the
"influence martingale". The influence martingale satisfies a $ 1d $ stochastic
differential equation enslaved to the ones governing the quantum trajectories.
Our interpretation is that the influence martingale models interference
effects between distinct realizations of quantum trajectories at strong
system-environment coupling.
Our result proves the existence of a Markovian quantum trajectory picture in
the Hilbert space of the system for completely bounded divisible dynamical
maps. Furthermore, our result provides a new avenue to numerically integrate
systems with large numbers of degrees of freedom by naturally extending the
existing theory.
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