Classical Limit: Dissipation of Spekkens' Generalised Contextuality under Decoherence

arXiv:2605.09558v3 Announce Type: replace Abstract: When does a decohering quantum system become classical? Generalised noncontextuality gives one criterion, for scenarios rich enough in preparations: a system is classical once its statistics admit an underlying model in which operationally indistinguishable procedures are physically identical. Where it crosses depends not on the state and channel alone but on which preparations, transformations and measurements the experiment offers, and if every measurement is allowed there is no crossing. For any pairwise unbiased bases in any dimension, given preparations holding their eigenstates and surrounding the maximally mixed state, the question reduces to a finite linear program; for a qudit of odd prime dimension $d$ restricted to the stabiliser subtheory, with one depolarised magic state, we solve it in closed form. With preparations and measurements alone the qutrit strange state is classical at zero noise; with the Clifford gates added, each channel represented once, it crosses at $3/5$; and with a random gate represented, as Spekkens' treatment asks, by the matching mixture of stochastic maps, at $3/4$. A Clifford orbit of assignments supports such a representation only if it has $d^2$ members, leaving, in every odd prime dimension, only Gross's discrete Wigner function: the crossing sits where it stops being negative.

Abstract:When does a decohering quantum system become classical? Generalised noncontextuality gives one criterion, for scenarios rich enough in preparations: a system is classical once its statistics admit an underlying model in which operationally indistinguishable procedures are physically identical. Where it crosses depends not on the state and channel alone but on which preparations, transformations and measurements the experiment offers, and if every measurement is allowed there is no crossing. For any pairwise unbiased bases in any dimension, given preparations holding their eigenstates and surrounding the maximally mixed state, the question reduces to a finite linear program; for a qudit of odd prime dimension $d$ restricted to the stabiliser subtheory, with one depolarised magic state, we solve it in closed form. With preparations and measurements alone the qutrit strange state is classical at zero noise; with the Clifford gates added, each channel represented once, it crosses at $3/5$; and with a random gate represented, as Spekkens' treatment asks, by the matching mixture of stochastic maps, at $3/4$. A Clifford orbit of assignments supports such a representation only if it has $d^2$ members, leaving, in every odd prime dimension, only Gross's discrete Wigner function: the crossing sits where it stops being negative.

24+11 pages, 2 figures. Erroneous KD/Wigner claims fixed, three subtheory cases differentiated, numerics added

Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)

arXiv:2605.09558 [quant-ph]

(or arXiv:2605.09558v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.09558 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

Classical Limit: Dissipation of Spekkens' Generalised Contextuality under Decoherence

Subiecte conexe