2020/02/29 by Yuxiang Yang, Giulio Chiribella, Masahito Hayashi
Computer Science · Physics and Astronomy · #Limit (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum capacity #Quantum computer #Quantum information #Quantum information science #Qubit #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1109/jsait.2020.3016061
published as IEEE Journal on Selected Areas in Information Theory, vol. 1, no. 2, pp. 387-400 (2020) · 9 pages, 4 figures plus appendix; published version
openalex publication_date 2020/08/01 · openalex created_date 2020/08/18 · arxiv created 2020/10/26 · arxiv updated 2020/10/27 · openalex updated_date 2026/08/05
A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer. An important problem is to determine the minimum amount of communication needed to specify the desired computation. Here we extend this problem to the quantum domain, analyzing the total amount of (classical and quantum) communication needed by a server in order to accurately execute a quantum process chosen by a client from a parametric family of quantum processes. We derive a general lower bound on the communication cost, establishing a relation with the precision limits of quantum metrology: if a v-dimensional family of processes can be estimated with mean squared error n-βby using n parallel queries, then the communication cost for n parallel executions of a process in the family is at least (β v/2 - ε) logn qubits at the leading order in n, for every ε > 0. For a class of quantum processes satisfying the standard quantum limit (β = 1), we show that the bound can be attained by transmitting an approximate classical description of the desired process. For quantum processes satisfying the Heisenberg limit (β = 2), our bound shows that the communication cost is at least twice as the cost of communicating standard quantum limited processes with the same number of parameters.