Min-entropy and quantum key distribution: Nonzero key rates for ''small'' numbers of signals
- Institute for Theoretical Physics III, Heinrich-Heine-Universitaet Duesseldorf, D-40225 Duesseldorf (Germany)
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals by evaluating the quantum conditional min-entropy explicitly. The min-entropy for a classical random variable is the negative logarithm of the maximal value in its probability distribution. The quantum conditional 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 nonzero 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 nonzero key rates for only 10{sup 4}-10{sup 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.
- OSTI ID:
- 21537146
- Journal Information:
- Physical Review. A, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevA.83.022330; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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