The Ruskai-Audenaert conjecture & equipartitions of positive operators

• URL: http://arxiv.org/abs/2607.23066v1
• Date: Sat, 25 Jul 2026 06:23:15 GMT
• Title: The Ruskai-Audenaert conjecture & equipartitions of positive operators
• Abstract summary: 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.<n>We prove the strong conjecture in all dimensions for a set of channels of nonzero measure, including all cq- and qc-channels.<n>We also prove the weak conjecture for all qutrit channels, along with further results on convex decompositions of quantum channels.
• Score: 3.5808917363708734
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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