quantum information

Exact Incompatibility-Breaking Criterion for Unital Qubit Channels

arXiv:2607.27757

summary

The paper derives the exact condition under which unital qubit channels make all POVMs jointly measurable, showing that projective measurements set the boundary, and uses this to determine the precise steering limits for two‑qubit states with maximally mixed marginals, while also providing a sufficient incompatibility‑breaking condition for nonunital channels.

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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Topics & keywords

#quantum channels#joint measurability#quantum steering#qubit systems#POVMsunital qubit channelincompatibility-breaking criterionprojective measurementsWerner statesparent POVM