Dilation theorem for continuum quantum stochastic processes

arXiv:2609.35403 · quant-ph, math-ph, math.MP · Submitted 2026-09-28 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-28

Updated: 2026-09-28

Comments: 7 pages + 28 page SM, 1 figure. Comments welcome!

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 22× in this paper · explained in 2 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Stochastic Dynamics — 3× in this paper · explained in 2 episodes
• Non-Markovian Dynamics — 2× in this paper · explained in 5 episodes
• Non-Markovianity — 2× in this paper · explained in 3 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Process tomography — 1× in this paper · explained in 2 episodes
• Quantum Trajectories — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Using the Environment to Understand non-Markovian Open Quantum Systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• An operational continuum limit of quantum combs
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Continuous operations on non-Markovian processes
• Continuous Matrix Product States for Quantum Fields
• The role of the rigged Hilbert space in Quantum Mechanics
• On the sampling complexity of open quantum systems
• Parameters estimation by fitting correlation functions of continuous quantum measurement
• Deterministic Equations for Feedback Control of Open Quantum Systems
• Time-averaged continuous quantum measurement

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