The Quantum Cohering Power of Local Channels*

The resource theory of quantum coherence studies coherence as a fundamental feature of quantum systems that can be converted from one form to another. Similar to the resource theory of entanglement, different measures of coherence have been proposed. The cohering power of a quantum channel can be defined, which is the maximum amount of coherence the channel can generate over all inputs. In this talk we show that the cohering power of certain channels can be increased when acting one half of an entangled state. In other words, the channel is able to generate more coherence on the joint system than on just the subsystem that it acts.

We then explore the connection between coherence and entanglement more closely. Specifically, we consider the problem of maximally increasing or decreasing the coherence of a bipartite state by local unitaries (LU). We show that when acting on two-qubit pure states, LU is just as powerful as nonlocal unitaries for increasing the coherence. In contrast, for decreasing the coherence (i.e. decoherence), LU is strictly weaker than nonlocal unitaries. We then compare the amount of decoherence that can be achieved by local unitaries to the amount of entanglement in the state.