A study about complete cohering/decohering power with ancillary system.

In this talk we will discuss the cohering/decohering power of a quantum operation which quantifies the maximum amount of coherence which can be generated/eliminated through that operation taken over all input states.
Complete cohering/decohering power (CCP and CDP respectively) of an operation is defined as cohering power of the product of the original operation and an identical operation on ancillary system. In our talk we will compare the properties of CCP and CDP with the general cohering/decohering power when only one system is considered.

We first observe that the CCP with L1 measure is not the same with general cohering power, or even not bounded. Taking dimension to be a large number, CCP increases unboundedly too. In contrast, for the relative entropy measure, the two cohering powers have the same value.
Then we consider the decohering power. Here we will have an unexpected result. For L1 measure, CDP does not have a boundary again. On the other hand, CDP with the relative entropy measure is larger than the general decohering power which can be seen with an entangled input state. This result strongly implies that entanglement helps CDP exceed the general cohering power. We will conclude with some open problems.