Dresden 2011 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 33: Quantum Information: Quantum Communication 2

Q 33.6: Talk

Wednesday, March 16, 2011, 15:45–16:00, SCH A118

Non-zero key rates for “small” numbers of signals using the min-entropy — •Sylvia Bratzik, Markus Mertz, Hermann Kampermann, and Dagmar Bruß — Institute for Theoretical Physics III, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany

We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly [1]. The min-entropy can be expressed in terms of the guessing probability [2], which we calculate for different d-dimensional QKD protocols. We compare these key rates to previous approaches using the von Neumann entropy [3] and find non-zero key rates for only 10⁴−10⁵ 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.

S. Bratzik et al., arXiv:1011.1190 [quant-ph].
R. König, R. Renner, and C. Schaffner, IEEE Trans. Inf. Th. 55, 4337 (2009), arXiv:0807.1338 [quant-ph].
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