Local Measurement Theory for Quantum Cellular Automata
Abstract
The formulation of quantum measurements compatible with relativistic causality is obstructed by the tension between the locality of observable algebras and the dynamical state transformations induced by measurement processes. We develop a local measurement theory for quantum cellular automata, lattices of finite-dimensional quantum systems with a causal reversible dynamics evolving in discrete time steps. Measurement processes are described by localized completely positive maps and organized into operational measurement protocols, finite non-adaptive sequences of local instruments distributed across the causal cone induced by the automaton local dynamics. Each protocol induces an effective measurement on the initial time slice, whose support is constrained by the causal structure generated by the automaton. Non-local measurement effects therefore arise through causal propagation and composition of local operations, rather than from primitive non-local interventions or instantaneous collapse prescriptions. We establish the corresponding spatial support bounds and characterize the resulting measurement architecture. As an explicit example, we construct a two-step protocol for a one-dimensional nearest-neighbour qubit automaton which, for suitable automaton parameters, realizes a Bell-basis projective measurement on two neighbouring sites after coarse-graining of the local outcomes. Away from this point, the same protocol generates a continuous family of deformed Bell measurements whose entanglement and stabilizer Rényi non-classicality can be quantified explicitly. The framework thus provides a causally consistent operator-algebraic mechanism for synthesizing spatially extended quantum measurements from strictly local operations.
Related
- Thermalization with Gaussian Quantum Cellular Automata
- Fermionic quantum cellular automata in 2d are trivial
- Non-abelian quantum cellular automata: 1+1-dimensional SU(2) Yang--Mills with fermions
- Quantum Cellular Automata on Symmetric Subalgebras
- Non-Clifford quantum cellular automata from invertible topological quantum field theories
BibTeX
@misc{brambilla2026local,
title = {{Local Measurement Theory for Quantum Cellular Automata}},
author = {Tommaso Brambilla and Alessandro Tosini and Paolo Perinotti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26587},
eprint = {2610.26587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26587},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local Measurement Theory for Quantum Cellular Automata
AU - Tommaso Brambilla
AU - Alessandro Tosini
AU - Paolo Perinotti
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26587
UR - https://arxiv.org/abs/2610.26587
AB - The formulation of quantum measurements compatible with relativistic causality is obstructed by the tension between the locality of observable algebras and the dynamical state transformations induced by measurement processes. We develop a local measurement theory for quantum cellular automata, lattices of finite-dimensional quantum systems with a causal reversible dynamics evolving in discrete time steps. Measurement processes are described by localized completely positive maps and organized into operational measurement protocols, finite non-adaptive sequences of local instruments distributed across the causal cone induced by the automaton local dynamics. Each protocol induces an effective measurement on the initial time slice, whose support is constrained by the causal structure generated by the automaton. Non-local measurement effects therefore arise through causal propagation and composition of local operations, rather than from primitive non-local interventions or instantaneous collapse prescriptions. We establish the corresponding spatial support bounds and characterize the resulting measurement architecture. As an explicit example, we construct a two-step protocol for a one-dimensional nearest-neighbour qubit automaton which, for suitable automaton parameters, realizes a Bell-basis projective measurement on two neighbouring sites after coarse-graining of the local outcomes. Away from this point, the same protocol generates a continuous family of deformed Bell measurements whose entanglement and stabilizer Rényi non-classicality can be quantified explicitly. The framework thus provides a causally consistent operator-algebraic mechanism for synthesizing spatially extended quantum measurements from strictly local operations.
ER -