No-signaling Quantum Key Distribution: A Straightforward Approach

Details No-signaling Quantum Key Distribution: A Straightforward Approach No-signaling Quantum Key Distribution: A Straightforward Approach

2012-02-17

arxiv.org/abs/1202.3822v1

Physics

Quantum Physics

7 pages, 2 figures

Scientific paper

We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints. Assuming an individual attack, we consider all possible joint probabilities. First we suppose temporarily that Eve (an eavesdropper) is restricted to binary outcomes. We impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using convex optimization, we find the maximum mutual information $I_{BE}^{max}(2)$ between Bob (a user) and a binary-restricted Eve. Then, by considering a certain coarse graining mapping, we show how to get a bound on $I_{BE}^{max}$, the maximal mutual information between Bob and Eve, whose number of outcomes is not restricted, from the quantity $I_{BE}^{max}(2)$. Using the Csisz\'ar-K\"orner formula and the calculated bound, we obtain the key generation rate.

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