ERROR-REJECTING BENNETT–BRASSARD–MERMIN QUANTUM KEY DISTRIBUTION PROTOCOL BASED ON LINEAR OPTICS OVER A COLLECTIVE-NOISE CHANNEL

Quantum entanglement is an important element of quantum information processing. Sharing entangled quantum states between two remote parties is a precondition of most quantum communication schemes. We will show that the protocol proposed by Yamamoto et al. (Phys. Rev. Lett.95 (2005) 040503) for transmitting single quantum qubit against collective noise with linear optics is also suitable for distributing the components of entanglements with some modifications. An additional qubit is introduced to reduce the effect of collective noise, and the receiver can take advantage of the time discrimination and the measurement results of the assistant qubit to reconstruct a pure entanglement with the sender. Although the scheme succeeds probabilistically, the fidelity of the entangled state is almost unity in principle. The resource used in our protocol to get a pure entangled state is finite, which establishes entanglement more easily in practice than quantum entanglement purification. Also, we discuss its application in quantum key distribution over a collective channel in detail.