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arxiv: 2605.15036 · v1 · pith:MU7QAWYB · submitted 2026-05-14 · quant-ph

Excitation Flow, Positivity, and Fisher Information for Open Subsystems of an N-Qubit Network

Tommy Chin , Sarah Shandera This is my paper

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classification quant-ph
keywords excitation flowpositivitycomplete positivityquantum Fisher informationopen quantum subsystemsqubit networkssingle excitationpropagators
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The pith

A single transition amplitude controls excitation flow, positivity of all propagators, entanglement entropy, and quantum Fisher information in subsystems of an N-qubit network.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives closed-form propagators for any K-qubit subsystem inside a closed N-qubit network that conserves exactly one excitation. A single transition amplitude simultaneously sets the direction of excitation flow, whether each propagator is positive and completely positive, the entanglement entropy of the subsystem, and the quantum Fisher information about global parameters. Positivity and complete positivity coincide and depend only on the sign of that amplitude, which indicates whether the map contracts the state toward its fixed point, independent of subsystem size, coherence, or entanglement. The full ensemble of propagators then imposes constraints on global network properties that no single subsystem can access alone. For single-qubit cases the positivity domain contains states that the dynamics never reach, and the total Fisher information is smallest when future propagators are nonpositive.

Core claim

In an N-qubit network conserving one excitation, the closed-form propagator for any K-qubit subsystem is fixed by a transition amplitude whose sign alone determines whether the map is positive and completely positive exactly when it contracts states toward the fixed point; the same amplitude controls entanglement entropy of every subsystem and decomposes the quantum Fisher information over any interval into a bounded state contribution and a secular process contribution that reaches its minimum when all future propagators are nonpositive.

What carries the argument

The single transition amplitude that sets the direction of excitation flow between the subsystem and its complement.

If this is right

  • Positivity and complete positivity of every propagator coincide and are determined solely by the direction of excitation flow.
  • A propagator is positive and completely positive if and only if it contracts the subsystem state toward its fixed point.
  • The ensemble of propagators from all subsystems constrains global properties inaccessible to any single subsystem.
  • For single-qubit subsystems a band of states lies inside the positivity domain of every propagator yet is never visited by the dynamics.
  • The total quantum Fisher information over an observation window is minimal when all future propagators are nonpositive and near maximum when they are positive and completely positive.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Local measurements of excitation flow direction could suffice to certify positivity properties of the open dynamics without full tomography.
  • The link between flow sign and positivity may extend to networks conserving other quantities beyond a single excitation.
  • Small-N simulations or experiments could directly check whether the unvisited band inside the positivity domain appears in physical devices.

Load-bearing premise

The underlying N-qubit network is closed and conserves exactly one excitation.

What would settle it

An observation or simulation in a single-excitation conserving network of a propagator that remains positive without contracting states to the fixed point, or whose positivity depends on subsystem size or entanglement structure.

Figures

Figures reproduced from arXiv: 2605.15036 by Sarah Shandera, Tommy Chin.

Figure 1
Figure 1. Figure 1: FIG. 1: An eight-qubit network with all-to-all [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Dynamics along the orbit of a global pure [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Excitation-flow amplitude [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Action of the single-qubit dynamical map [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Classical and quantum contributions to the [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Fisher information [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Process, state, cross, and total contributions to the rescaled Fisher information [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

We derive closed-form propagators for any $K$-qubit subsystem of a closed $N$-qubit network with a single conserved excitation. A single transition amplitude simultaneously controls excitation flow between subsystems, the positivity and complete positivity of every propagator, the entanglement entropy of every subsystem, and the quantum Fisher information for global parameters. Positivity and complete positivity coincide, determined solely by the direction of excitation flow, independently of subsystem size, coherence, or entanglement structure. A propagator is positive and completely positive if and only if it contracts the subsystem state toward its fixed point. The ensemble of propagators collectively constrains global properties inaccessible to any single subsystem. For single-qubit subsystems, we characterize the ensemble's fixed-point distribution and domain of positivity, finding a band of states that lies inside the positivity domain of every propagator yet is never visited by the physical dynamics. The quantum Fisher information decomposes into state and process contributions over any observation window $[t_1,t_2]$, with the state contribution bounded while the process contribution grows secularly. The total Fisher information is minimal when all future propagators are nonpositive and not completely positive, and near its maximum when they are positive and completely positive.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript derives closed-form propagators for arbitrary K-qubit subsystems of a closed N-qubit network conserving exactly one excitation. It asserts that a single transition amplitude simultaneously governs excitation flow between subsystems, the positivity and complete positivity of every propagator, subsystem entanglement entropy, and the quantum Fisher information for global parameters. Positivity and complete positivity are shown to coincide, to be equivalent to contraction toward the subsystem fixed point, and to depend only on the sign of the relevant transition amplitude, independently of subsystem size, coherence, or entanglement structure. The ensemble of propagators is shown to constrain global properties inaccessible to any individual subsystem. For single-qubit cases the fixed-point distribution and positivity domain are characterized, revealing a band of states inside every propagator's positivity domain that is never reached by the physical dynamics. The quantum Fisher information over any interval [t1,t2] decomposes into a bounded state contribution and a secularly growing process contribution, with the total minimized when future propagators are nonpositive and not completely positive.

Significance. If the closed-form derivations hold, the work supplies an exactly solvable family of open-subsystem dynamics in which local positivity, flow, and metrological quantities are controlled by a single parameter whose sign is fixed by the global conservation law. The explicit equivalence between positivity, complete positivity, and contraction, together with the identification of an unvisited band inside the positivity domain and the decomposition of Fisher information, provides concrete, falsifiable relations that could be tested in engineered quantum networks and that clarify the interplay between local open dynamics and global constraints.

minor comments (2)
  1. The notation for the single transition amplitude and the precise definition of the fixed point for a general K-qubit subsystem should be introduced with an explicit equation in the main text (rather than only in the abstract) to make the independence claims immediately verifiable.
  2. Figure captions for the single-qubit positivity domain and the unvisited band should state the numerical values of the transition amplitude used and the precise time window over which the band is shown to remain unvisited.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the detailed and positive summary of our manuscript, as well as the recommendation for minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

Derivation self-contained from explicit single-excitation propagators

full rationale

The paper constructs closed-form propagators for K-qubit subsystems directly from the global dynamics of the closed N-qubit network in the single-excitation manifold. Positivity, complete positivity, their coincidence, and dependence solely on the sign of the transition amplitude are then shown to follow from the contraction properties of those explicit propagators toward fixed points. No load-bearing step reduces by definition or by self-citation to its own inputs; the ensemble constraints on global properties and the Fisher-information decomposition are likewise obtained by direct calculation from the derived propagators. The derivation therefore remains independent of the target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the model of a closed N-qubit network with exactly one conserved excitation is presupposed but not detailed.

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