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Published on: July 19, 2016
Hamiltonian and double-bracket flow formulations of quantum measurements
Aaron Villanueva1,2, Luis Pedro Garćia-Pintos2
1Faculty of Science, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
Summary
We unified quantum measurement, Hamiltonian dynamics, and gradient flows using stochastic Hamiltonians. This framework reveals wavefunction collapse as coarse-grained dynamics, enabling new quantum feedback control strategies.
Area of Science:
- Quantum Physics
- Quantum Information Theory
- Mathematical Physics
Background:
- Quantum measurements are typically described by non-unitary processes.
- Hamiltonian dynamics govern isolated quantum systems.
- Gradient flows describe systems minimizing potentials.
Purpose of the Study:
- To unify quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows.
- To provide stochastic Hamiltonians for continuous quantum measurements.
- To reinterpret wavefunction collapse and design novel feedback processes.
Main Methods:
- Deriving explicit expressions for stochastic Hamiltonians.
- Interpreting wavefunction collapse as coarse-grained stochastic Hamiltonian dynamics.
- Formulating measurement dynamics as double-bracket gradient flows.
Main Results:
- Stochastic Hamiltonians yield state dynamics identical to continuous quantum measurements.
- Wavefunction collapse is equivalent to coarse-grained Hamiltonian dynamics or gradient flows.
- Feedback processes can be designed for ground state preparation and entanglement stabilization.
Conclusions:
- Quantum measurement dynamics can be unified with Hamiltonian dynamics and gradient flows.
- Wavefunction collapse has a novel interpretation as coarse-grained stochastic dynamics.
- The framework facilitates the design of advanced quantum feedback control strategies.
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