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Quantum signal propagation in depolarizing channels

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1 Author(s)
Pippenger, N. ; Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada

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) ⩽ (1-p)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

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 1 )