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Detecting mixed-unitary quantum channels is NP-hard
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A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not that channel is a mixed-unitary channel. This hardness result holds even under the assumption that the channel is not within an inverse-polynomial distance (in the dimension of the space upon which it acts) of the boundary of the mixed-unitary channels.
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Pretty-good simulation of all quantum measurements by projective measurements
Every POVM on C^d becomes projectively simulable after depolarizing with dimension-independent visibility c = 0.02, and can be simulated with postselection probability 1/8 using only a single auxiliary qubit.
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