Using and reusing coherence to realize quantum processes

Understand

Coherent superposition is a key feature of quantum mechanics that underlies the advantage of quantum technologies over their classical counterparts.

• Recently, coherence has been recast as a resource theory in an attempt to identify and quantify it in an operationally well-defined manner.
• Here we study how the coherence present in a state can be used to implement a quantum channel via incoherent operations and, in turn, to assess its degree of coherence.
• We introduce the robustness of coherence of a quantum channel---which reduces to the homonymous measure for states when computed on constant-output channels---and prove that: i) it quantifies the minimal rank of a maximally coherent state required to implement the channel; ii) its logarithm quantifies the amortized cost of implementing the channel provided some coherence is recovered at the output; iii) its logarithm also quantifies the zero-error asymptotic cost of implementation of many independent copies of a channel.