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Pure-state quantum trajectories for general non-Markovian systems do not exist
Howard M Wiseman1, J M Gambetta
1Centre for Quantum Dynamics, School of Science, Griffith University, Nathan 4111, Australia.
Physical Review Letters
|October 15, 2008
Summary
Non-Markovian stochastic Schrödinger equations do not generate true single system trajectories. While solutions represent conditioned states at specific times, their sequential combination forms a fictional trajectory, challenging prior interpretations.
Area of Science:
- Quantum mechanics
- Quantum information theory
- Statistical physics
Background:
- Non-Markovian stochastic Schrödinger equations (SSEs) are used to model open quantum systems.
- Their interpretation, particularly regarding single-system trajectories under continuous measurement, has been debated.
- A recent claim suggested SSEs generate "true single system trajectories."
Purpose of the Study:
- To rigorously analyze the interpretation of non-Markovian stochastic Schrödinger equations.
- To evaluate the validity of claims that these equations produce "true single system trajectories."
Main Methods:
- Mathematical analysis of the Diósi non-Markovian stochastic Schrödinger equation.
- Conceptual examination of the definition of "trajectory" in the context of quantum measurement.
Main Results:
- The proof that non-Markovian SSEs generate "true single system trajectories" is fundamentally flawed.
- Solutions to these equations represent valid conditioned states at specific time instances.
- Connecting these time-sliced states sequentially does not constitute a physically real trajectory.
Conclusions:
- The interpretation of non-Markovian SSEs as generating "true single system trajectories" is incorrect.
- The sequential solutions of these equations should not be viewed as a continuous physical process.
- This finding necessitates a re-evaluation of the foundational understanding of quantum trajectories in open systems.
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