Quantum Signal Propagation in Depolarizing Channels Nicholas Pippenger Abstract: Let X be an unbiassed random bit, let Y be a qubit whose mixed state depends on X, and let the qubit Z be the result of passing Y through a depolarizing channel, which replaces Y with a completely random qubit with probability p. We measure the quantum mutual information between X and Y by T(X; Y) = S(X) + S(Y) - S(X,Y), where S(...) denotes von Neumann's entropy. (Since X is a classical bit, the quantity T(X; Y) agrees with Holevo's bound chi(X; Y) to the classical mutual information between X and the outcome of any measurement of Y.) We show that T(X;Z) <= (1-p)^2 T(X;Y). This generalizes an analogous bound for classical mutual information due to Evans and Schulman, and provides a new proof of their result.
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