2018/05/31 by María García Díaz, Kun Fang, Xin Wang +4 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Coherence (philosophical gambling strategy) #Coherence time #Coherent states #Combinatorics #Computer science #Logarithm #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum entanglement #Quantum mechanics #Quantum state #Qubit #Robustness (evolution) #Superposition principle #Theoretical computer science #Topology (electrical circuits) #Unitary state #quant-ph
paper · pdf · doi:10.22331/q-2018-10-19-100
published as Quantum 2, 100 (2018) · 8 pages (main text) + 9 pages (supplementary material). Comments welcome. v2: minor edits to the introduction. v3: version accepted for publication in Quantum
arxiv created 2018/10/16 · openalex publication_date 2018/10/19 · arxiv updated 2018/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 every pure coherent state in dimension larger than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2</mml:mn></mml:math>, however weakly so, turns out to be a valuable resource to implement some coherent unitary channel. We illustrate our findings for the case of single-qubit unitary channels.