Security analysis of a basis-independent scheme for quantum cryptography

Abstract

We propose a rotationally-invariant quantum key distribution (QKD) scheme with a pair of orthogonal qubit trines. This double trine scheme uses mixed product states of a singlet and a random qubit. The measurement outcomes of the scheme are independent of the reference frames chosen by Alice or Bob. This scheme produces two sets of keys, a bit key and a trit key. The noiseless mutual information between Alice and Bob is approximately 0.573 (98% of the Shannon limit), exceeding by a considerable amount that of other trine-based schemes such as PBC00, which attains 85.5% of the Shannon limit. The security analysis reveals an asymmetry in Eve's conditioned ancillas for Alice and Bob resulting from the asymmetry in key generation. We find the absolute noise thresholds are e=0.17 for the bit case and e=0.15 for the trit case, which Eve attains by optimizing a single free parameter.