Quantum key distribution by phase flipping of coherent states of light

Abstract: In this paper we present quantum key distribution protocol that, instead of single qubits, uses mesoscopic coherent states of light $|\alpha\rangle$ to encode bit values of a randomly generated key. Given the reference value $\alpha\in\mathbb C$, and a string of phase rotations each randomly taken from a set of $2M$ equidistant phases, Alice prepares a quantum state given by a product of coherent states of light, such that a complex phase of each pulse is rotated by the corresponding phase rotation. The encoding of $i$-th bit of the key $r=r_1 \dots r_\ell$ is done by further performing phase rotation $r_i \pi$ (with $r_i = 0,1$) on the $i$-th coherent state pulse. In order to protect the protocol against the man-in-the-middle attack, we introduce a verification procedure, and analyse the protocol's security using the Holevo bound. We also analyse the possibility of beam splitting-like and of collective attacks, showing the impossibility of the former and, in the case of our protocol, the inadequacy of the latter. While we cannot prove full perfect security against the most general attacks allowed by the laws of quantum mechanics, our protocol achieves faster quantum key distribution, over larger distances and with lower costs, than the single-photon counterparts, maintaining at least practical security against the current and the near future technologies.