Sufficient Channels and Measurements

Максим Евгеньевич Широков

We consider the nontrivial class of infinite dimensional quantum channels, characterized by the finiteness of the Holevo capacity. The sufficient conditions of existence of an optimal measure are obtained and examples of channels with no optimal measure are constructed.

Yujie Zhang

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.

Edward B. Manoukian

Luigi Accardi, Igor Vasil'evich Volovich, Yun Gang Lu

David S. Simon

Yu Jing Guo, Jinchuan Hou

Measurement-induced nonlocality is a measure of nonlocality introduced recently by Luo and Fu. We present here sufficient and necessary conditions for a quantum state for which this quantity is equal to zero. Furthermore it is shown that for such a state ?ab with any local channel acting on Ha cannot create measurement-induced nonlocality if and only if either it is a completely contractive channel or it is a nontrivial isotropic channel. For the qubit case this property is an additional characteristic of the completely contractive channel or the commutativity-preserving unital channel.