paper

Using and reusing coherence to realize quantum processes

arXiv:1805.04045 · doi:10.22331/q-2018-10-19-100

Abstract

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. We also consider the generalized problem of imperfect implementation with arbitrary resource states. Using the robustness of coherence, we find that in general a quantum channel can be implemented without employing a maximally coherent resource state. In fact, we prove that \textit{every} pure coherent state in dimension larger than , however weakly so, turns out to be a valuable resource to implement \textit{some} coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.

8 pages (main text) + 9 pages (supplementary material). Comments welcome. v2: minor edits to the introduction. v3: version accepted for publication in Quantum

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