The Spectral Bottleneck Constraint: A No-Go Theorem for Aggregate Asymptotic Rate Laws, Validated on IBM Quantum Hardware

Many systems admit observables that can be decomposed into exponentially decaying modes.

In such systems, the asymptotic exponential rate is not controlled by total amplitude, mode

count, particle number, average rate, or any other aggregate that fails to determine the slowest

nonvanishing decay component; it is controlled by the bottleneck mode. We formalize this as a

finite-dimensional constraint theorem and prove a no-go result: any rate law that depends only on

an aggregate that can be held fixed while the bottleneck changes cannot be a universal asymptotic

rate predictor. We give a rigorous application to finite-dimensional Markovian dephasing, where

the decay of supported coherences is governed by the minimum decoherence rate among them. An

explicit n-qubit family |ψr⟩ = (|0

n⟩ + |1

r0

n−r

⟩)/

√

2 with r = 1, . . . , n has identical particle count

and asymptotic rates differing by a factor of n, falsifying particle-count-only predictors. We test

the structural content of the constraint experimentally on ibm torino using full quantum state

tomography of 3-qubit GHZ and Cluster states across five idle delays. The predicted leading-order

law DM = AρW≤D∗ + O(W3/2

) holds linearly to R2 > 0.999 on Cluster and R2 > 0.99 on GHZ;

the calibration-independent ratio of regression slopes matches the parameter-free Kubo–Mori

prediction to 9.1%, ruling out alternative monotone kernels in the Petz family. We then discuss

collapse-type master equations as a conditional application and machine-learning settings as

spectral analogues. The contribution is mathematical (a constraint theorem) and experimental

(a structural demonstration on real quantum hardware), not a new dynamical mechanism.