• Accepted Paper

Excitation flow, positivity, and Fisher information for open subsystems of an N-qubit network

Tommy Chin and Sarah Shandera

Phys. Rev. A - Accepted 15 October, 2026

DOI: https://doi.org/10.1103/qkr6-slbp

Abstract

An observer of an autonomous quantum system has no privileged initial time, reference state, or subsystem boundary, so the natural framework for the open dynamics is an ensemble of propagators over many subsystems and time windows. We derive such an ensemble analytically for a closed N-qubit network with homogeneous all-to-all coupling and a single conserved excitation, giving the propagator of any K-qubit subsystem over any time window. To keep the analytical calculation tractable, we exclude excitation flow in sectors of two or more excitations. A single transition amplitude underlies excitation flow, positivity, entanglement entropy, and quantum Fisher information. Positivity and complete positivity reduce to the direction of the excitation flow, so the two coincide for every subsystem size. Both hold for a propagator if and only if it contracts the subsystem state toward a fixed point shared by its dynamical class. Neither the entanglement entropy nor its change over the time window corresponds to this contraction. The ensemble constrains global parameters inaccessible to any single subsystem, such as the size and coupling of the rest of the network. A band of states lies inside the domain of positivity of every single-qubit propagator, yet the reduced state never visits the band. In completely positive divisible dynamics, by contrast, any propagator may act on any state. The quantum Fisher information decomposes into a bounded state contribution and a secularly growing process contribution. The total is minimal when all future propagators are nonpositive and near its maximum when they are positive.

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