2008/04/30 by Bill Rosgen · 19 citations
Computer Science · Physics and Astronomy · #Additive function #Circular ensemble #Complexity and Algorithms in Graphs #Entropy (arrow of time) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum channel #Quantum phase estimation algorithm #Quantum relative entropy #Unitary matrix #Unitary state #quant-ph
paper · pdf · doi:10.1063/1.2992977
published in Journal of Mathematical Physics 49(10) (American Institute of Physics) · 18 pages, 2 figures, typos fixed, introduction expanded
openalex publication_date 2008/10/01 · arxiv created 2008/10/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output p-norm can be equivalently restated in terms of random unitary channels. This is done by constructing a random unitary approximation to a general quantum channel. This approximation can be constructed efficiently, and so it is also applied to the computational problem of distinguishing quantum circuits. It is shown that the problem of distinguishing random unitary circuits is as hard as the problem of distinguishing general mixed-state circuits, which is complete for the class of problems having quantum interactive proof systems.