Markov Constraints Enhance Identifiability in Quantum Shadow Inversion

Abstract:We study quantum shadow inversion under Markovian locality constraints for four-partite systems arranged along the chain $A$--$B$--$C$--$D$. The goal is to reproduce the expectation value of a fixed endpoint observable $O_{AD}$ after an unknown global unitary, without requiring full unitary inversion. We formulate the task using Markov-admissible supermaps and introduce the Markov-implementable centralizer to describe the remaining endpoint gauge freedom. We show that unrestricted endpoint post-processing is too broad, and impose an endpoint-local refinement. Under this condition, every implementable endpoint unitary must factorize across $A|D$, so the Markov constraint strictly reduces the centralizer-induced shadow ambiguity whenever the full centralizer contains non-product unitaries. This provides a structural mechanism by which Markov locality enhances identifiability in quantum shadow inversion.

Quantum Physics (quant-ph); Quantum Algebra (math.QA)

arXiv:2608.21765 [quant-ph]

(or arXiv:2608.21765v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.21765 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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