(GQR51/OperA_3) Contraction of Admissibility Distance under Amplitude Damping and Non-Unital Quantum Noise
Description
Resource-theoretic measures of quantum channels are useful only if
they remain mathematically controlled under physically realistic noise. We
investigate the behaviour of the operational admissibility distance under
non-unital completely positive trace-preserving maps. Using amplitude
damping as a canonical model of energy relaxation, we show that although
non-unital channels possess an affine component in their Bloch representation, this contribution cancels identically on trace-annihilating channel
differences, leaving contraction governed solely by the linear action on
the traceless operator subspace. This yields an explicit contraction coefficient, a bipartite suppression factor, and an exponential persistence law
under repeated local noise. These results extend the admissibility-distance
framework from idealized unital channels to dissipative noise models, establishing mathematically controlled resource contraction in physically
realistic settings and providing a rigorous foundation for analysing dynamical nonlocality under energy relaxation.
Series information
v2 The principal changes are:
Programme positioning clarified.
The manuscript is now explicitly presented as part of the OperATM (Operational Admissibility) programme, with its role within the broader channel-resource framework stated clearly in the Introduction.
Mathematical treatment strengthened.
A formal Lemma proving affine cancellation on the traceless Hermitian subspace has been added.
The amplitude-damping contraction theorem has been expanded with a complete proof rather than a sketch.
Structural interpretation improved.
The distinction between affine drift and contraction on the traceless sector is now discussed explicitly, clarifying why the contraction coefficient depends only on the linear Bloch action.
Engineering interpretation expanded.
A dedicated discussion relates the contraction law to physical relaxation and persistence of dynamical nonlocal resources under repeated local noise.
Presentation modernised.
The introduction has been rewritten.
References have been updated and expanded.
Acknowledgements, data availability, competing interests, and AI-use disclosures have been added for transparency.
Notation and exposition improved.
The manuscript has been reorganised for readability, with clearer separation of:
the amplitude-damping model,
the contraction theorem,
bipartite contraction,
physical interpretation,
engineering relevance,
and conclusions
Full programme Index: https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md