Dilation theorem for continuum quantum stochastic processes
Abstract
Connecting mathematical formalism in open quantum systems to its underlying physics necessitates the notion of a dilation, a way to bridge stochastic dynamics with deterministic Schrödinger evolution on a larger space. Although dilations are well known in the literature for states, channels, and quantum combs, there is a substantial gap when it comes to the fully general setting of non-Markovian dynamics on a continuous interval. In an accompanying work, we introduce a continuous process tensor (cPT) framework wherein these processes are represented by vectors in multi-species bosonic Fock spaces of L2 functions. This accommodates all multi-time statistics of a quantum system on an interval. Here, we present a corresponding dilation theorem and show that all cPTs can be approximated arbitrarily well by an explicit closed description with system and environment coupled by a bounded Hamiltonian. As well as its physical appeal and demonstrating completeness of the framework, we show that such regular representations actually underpin the formalism, defining a dense subspace of all cPTs that is easy to handle. This leads to a continuum-suitable version of Choi duality, and permits the rigorous treatment of continuum controls.
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BibTeX
@misc{fuksa2026dilation,
title = {{Dilation theorem for continuum quantum stochastic processes}},
author = {Jonáš Fuksa and Clara Wassner and Jens Eisert and Gregory A. L. White},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35403},
eprint = {2609.35403},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35403},
}
RIS
TY - UNPB
TI - Dilation theorem for continuum quantum stochastic processes
AU - Jonáš Fuksa
AU - Clara Wassner
AU - Jens Eisert
AU - Gregory A. L. White
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35403
UR - https://arxiv.org/abs/2609.35403
AB - Connecting mathematical formalism in open quantum systems to its underlying physics necessitates the notion of a dilation, a way to bridge stochastic dynamics with deterministic Schrödinger evolution on a larger space. Although dilations are well known in the literature for states, channels, and quantum combs, there is a substantial gap when it comes to the fully general setting of non-Markovian dynamics on a continuous interval. In an accompanying work, we introduce a continuous process tensor (cPT) framework wherein these processes are represented by vectors in multi-species bosonic Fock spaces of L^2 functions. This accommodates all multi-time statistics of a quantum system on an interval. Here, we present a corresponding dilation theorem and show that all cPTs can be approximated arbitrarily well by an explicit closed description with system and environment coupled by a bounded Hamiltonian. As well as its physical appeal and demonstrating completeness of the framework, we show that such regular representations actually underpin the formalism, defining a dense subspace of all cPTs that is easy to handle. This leads to a continuum-suitable version of Choi duality, and permits the rigorous treatment of continuum controls.
ER -