Min-entropy and quantum key distribution: non-zero key rates for "small" numbers of signals
Abstract
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10^4-10^5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.
Keywords
Cite
@article{arxiv.1011.1190,
title = {Min-entropy and quantum key distribution: non-zero key rates for "small" numbers of signals},
author = {Sylvia Bratzik and Markus Mertz and Hermann Kampermann and Dagmar Bruß},
journal= {arXiv preprint arXiv:1011.1190},
year = {2011}
}
Comments
10 pages, 6 figures, changed plots due to the erratum of L. Sheridan and V. Scarani, Phys. Rev. A 83, 039901 (2011)