Additivity and Distinguishability of Random Unitary Channels

Abstract

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 that have quantum interactive proof systems.

18 pages, 2 figures, typos fixed, introduction expanded

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• Environment-Assisted Quantum State Restoration Via Weak Measurement
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• On the mixed-unitary rank of quantum channels
• Quantum state tomography with informationally complete POVMs generated in the time domain
• Detecting mixed-unitary quantum channels is NP-hard
• Ancilla dimension in quantum channel discrimination
• Capacities of Grassmann channels
• Simulation of open quantum systems via low-depth convex unitary evolutions
• Exact reduced dynamics for a qubit in a precessing magnetic field and in the contact with a heat-bath
• Channel discrimination power of bipartite quantum states
• Open system model for quantum dynamical maps with classical noise and corresponding master equations
• Simulation of open quantum systems on universal quantum computers