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This theoretical quant-ph paper recasts continuous quantum measurement and wavefunction collapse as coarse-grained stochastic Hamiltonian dynamics and as double-bracket gradient flows that minimise observable variance. Its practical relevance is in feedback control: the authors propose feedback schemes for ground-state and entanglement preparation, tested on a two-qubit system with imperfect measurements and delay. Readers working on quantum control and state preparation will find the unified framework useful, though the results are analytical and simulation-based rather than hardware demonstrations.
Hamiltonian and double-bracket flow formulations of quantum measurements
arXiv:2512.15412v3 Announce Type: replace Abstract: We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to those that happen during continuous quantum measurements. When such dynamical processes are integrated over sufficiently long time intervals, they yield the same results and statistics as during wavefunction collapse. That is, wavefunction collapse can be interpreted as coarse-grained (stochastic) Hamiltonian dynamics. Alternatively, wavefunction collapse can be interpreted as double-bracket gradient flows determined by derivatives of (stochastic) potentials defined in terms of observables with direct physical interpretations. The gradient flows minimize the variance of the monitored observable. Our derivations hold for general monitoring described by non-Hermitian jump processes. We show that such reinterpretations of measurement dynamics facilitate the design of feedback processes. In particular, we introduce feedback processes that yield deterministic double-bracket flow equations that prepare ground states of a target Hamiltonian, and state-agnostic feedback processes for state preparation. We apply the latter for entanglement stabilization of a two-qubit system considering a setup with imperfect measurements and feedback delay. We conclude by re-interpreting feedback processes as gradient flows with tilted fixed points.
Abstract:We introduce a framework that unifies quantum measurement dynamics, Hamiltonian dynamics, and double-bracket gradient flows. We do so by providing explicit expressions for stochastic Hamiltonians that produce state dynamics identical to those that happen during continuous quantum measurements. When such dynamical processes are integrated over sufficiently long time intervals, they yield the same results and statistics as during wavefunction collapse. That is, wavefunction collapse can be interpreted as coarse-grained (stochastic) Hamiltonian dynamics. Alternatively, wavefunction collapse can be interpreted as double-bracket gradient flows determined by derivatives of (stochastic) potentials defined in terms of observables with direct physical interpretations. The gradient flows minimize the variance of the monitored observable. Our derivations hold for general monitoring described by non-Hermitian jump processes. We show that such reinterpretations of measurement dynamics facilitate the design of feedback processes. In particular, we introduce feedback processes that yield deterministic double-bracket flow equations that prepare ground states of a target Hamiltonian, and state-agnostic feedback processes for state preparation. We apply the latter for entanglement stabilization of a two-qubit system considering a setup with imperfect measurements and feedback delay. We conclude by re-interpreting feedback processes as gradient flows with tilted fixed points.
24 pages, 7 figures. Added proof of stability for entanglement steering
arXiv:2512.15412 [quant-ph]
(or arXiv:2512.15412v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.15412 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1088/1361-6633/ae6fe9 Focus to learn more DOI(s) linking to related resources
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