Exact Incompatibility-Breaking Criterion for Unital Qubit Channels

• URL: http://arxiv.org/abs/2607.27757v1
• Date: Thu, 30 Jul 2026 06:55:37 GMT
• Title: Exact Incompatibility-Breaking Criterion for Unital Qubit Channels
• Abstract summary: We study when a noisy qubit channel renders all positive-operator-valued measures jointly measurable.<n>For every unital qubit channel, we derive the exact incompatibility-breaking criterion and prove that projective measurements already determine the boundary for arbitrary POVMs.
• Score: 29.850754213301368
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study when a noisy qubit channel renders all positive-operator-valued measures (POVMs) jointly measurable. For every unital qubit channel, we derive the exact incompatibility-breaking criterion and prove that projective measurements already determine the boundary for arbitrary POVMs. Through the steering--joint-measurability correspondence, this result gives the exact POVM-steering boundary for all two-qubit states with maximally mixed marginals, with the Werner states recovered as a special case. For nonunital qubit channels, we construct a generally asymmetric parent POVM and obtain an explicit sufficient incompatibility-breaking condition, which in turn yields a sufficient unsteerability criterion for arbitrary two-qubit states.

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