The Ruskai-Audenaert conjecture & equipartitions of positive operators

Abstract:Several open problems in quantum information theory can be formulated as equipartition problems for positive operators, asking for a decomposition into bounded-rank positive parts under uniform constraints. The existence problems for SIC-POVMs and MUBs are of this type, as is the Ruskai-Audenaert conjecture. We first show that certain problems of this form can be attacked using equivariant cohomology, and then present new results on the Ruskai-Audenaert conjecture. In its weak form, this conjecture asserts that every quantum channel admits a convex decomposition into a minimal number of generalized extreme points; in its strong form, one with equal weights. We prove the strong conjecture in all dimensions for a set of channels of nonzero measure, including all cq- and qc-channels, as well as for all channels with qubit inputs. We also prove the weak conjecture for all qutrit channels, along with further results on convex decompositions of quantum channels.

arXiv:2607.23066 [quant-ph]

(or arXiv:2607.23066v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.23066 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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