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Quantum trajectory framework for general time-local master equations.

Brecht Donvil1,2, Paolo Muratore-Ginanneschi3

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General master equations for open quantum systems can now be unraveled into quantum trajectories. This new method uses an "influence martingale" to extend quantum trajectory theory without adding computational complexity.

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Area of Science:

  • Quantum Physics
  • Open Quantum Systems
  • Quantum Information Theory

Background:

  • Master equations are fundamental for studying open quantum systems.
  • Lindblad-Gorini-Kossakowski-Sudarshan (LGKS) master equations can be unraveled into quantum trajectories, serving as both a theoretical tool and numerical method.
  • Existing methods are limited to specific forms of master equations.

Purpose of the Study:

  • To demonstrate that general time-local and trace-preserving master equations can also be unraveled into quantum trajectories.
  • To extend the theory of quantum trajectories beyond the LGKS form.
  • To provide a more versatile framework for analyzing open quantum systems.

Main Methods:

  • Developing a novel approach using a probability pseudo-measure termed the "influence martingale".
  • Showing that this influence martingale satisfies a stochastic differential equation.
  • Demonstrating that this framework applies to general time-local and trace-preserving master equations.

Main Results:

  • General time-local and trace-preserving master equations can be unraveled into quantum trajectories.
  • The unraveling is achieved by weighting averages with the influence martingale.
  • The influence martingale is governed by a stochastic differential equation enslaved to the quantum trajectories.

Conclusions:

  • The theory of quantum trajectories is extended to a broader class of master equations.
  • This extension does not increase the computational complexity of numerical simulations.
  • The influence martingale provides a new tool for understanding and simulating open quantum systems.