Physics – Quantum Physics
Scientific paper
2010-11-04
Phys. Rev. A 83, 022330 (2011)
Physics
Quantum Physics
10 pages, 6 figures, changed plots due to the erratum of L. Sheridan and V. Scarani, Phys. Rev. A 83, 039901 (2011)
Scientific paper
10.1103/PhysRevA.83.022330
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.
Bratzik Sylvia
Bruß Dagmar
Kampermann Hermann
Mertz Markus
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