Discretization of quantum pure states and local random unitary channel
msra(2010)
摘要
We show that a quantum channel $\mathcal{N}$ constructed by averaging over
$\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local
$\epsilon$-randomizing map with non-negative probability. The idea comes from a
small $\epsilon$-net construction on the higher dimensional unit sphere or
quantum pure states. By exploiting the net, we analyze the concentrative
phenomenon of an output reduced density matrix of the channel, and this
analysis imply that there exists a local random unitary channel, with
relatively small unitaries, generically.
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关键词
quantum physics,quantum channel
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