Secure quantum key distribution using squeezed states - art. no. 022309

We prove the security of a quantum key distribution scheme based on transmi ssion of squeezed quantum states of a harmonic oscillator. Our proof employ s quantum error-correcting codes that encode a finite-dimensional quantum s ystem in the infinite-dimensional Hilbert space of an oscillator, and prote ct against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squee ze factor e(r) = 1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and pri vacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.