Telescopic Relative Entropy

Details Telescopic Relative Entropy Telescopic Relative Entropy

2011-02-15

arxiv.org/abs/1102.3040v2

Physics

Mathematical Physics

15 pages, 4 figures; to be presented at TQC2011, Madrid, May 2011. V2: New proof of Theorem 4. Section added on telescoping th

Scientific paper

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm distance. We then exploit the same techniques to obtain a new and shorter proof of a lower bound on the relative Renyi entropies in terms of the trace norm distance, $\trace\rho^{1-p}\sigma^p \ge 1-(||\rho-\sigma||_1)/2$.

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