2018/04/30 by Zbigniew Puchała, Łukasz Pawela, Aleksandra Krawiec +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Bounded function #Computer science #Focus (optics) #Mathematical analysis #Mathematics #Norm (philosophy) #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum state #Simple (philosophy) #TRACE (psycholinguistics) #Unitary state #Upper and lower bounds #Von Neumann architecture #quant-ph
paper · pdf · doi:10.1103/physreva.98.042103
published as Phys. Rev. A 98, 042103 (2018) · 13 pages, 4 figures
openalex publication_date 2018/10/03 · arxiv created 2018/11/07 · arxiv updated 2018/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work, we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance between the measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product, the program finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.