Quantum Signal Propagation in Depolarizing Channels
Let X be an unbiased 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 (1948) entropy. (Since X is a classical bit, the quantity T(X; Y) agrees with Holevo's (1973) bound χ(X; Y) to the classical mutual information between X and the outcome of any measurement of Y.) We show that T(X; Z)2T(X; Y). This generalizes an analogous bound for classical mutual information due to Evans and Schulman (1993), and provides a new proof of their result.
© 2002 IEEE
Pippenger, N.; , "Quantum signal propagation in depolarizing channels," Information Theory, IEEE Transactions on , vol.48, no.1, pp.276-278, Jan 2002.