Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection

We propose efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. By these phase encodings, the probability of basis mismatch is reduced and total efficiency is increased. We also propose mixed-state protocols by omitting a part of classical communication steps in the efficient-phase-encoding protocols. The omission implies a reduction of information to an eavesdropper and possibly enhances the security of the protocols. We investigate the security of the protocols against individual beam splitting attack.

Figure 1

The pulse emitted from a light source (LD) is split into a strong local oscillator (LO) and a weak signal field by an asymmetric beam splitter (ABS). Alice applies her phase shift ${\varphi }_A$ to the signal and Bob applies his phase shift ${\varphi }_B$ to the LO. The signal and LO interfere at the 50:50 beam splitter (BS). The difference between the photon numbers of the output pulses of the BS is observed.

Figure 2

The quadrature distributions of correct-basis choice are shown. The solid curve peaked at $x=\alpha$ corresponds to the signal of Alice’s bit “1” and the dotted line peaked at $x=-\alpha$ corresponds to the signal of Alice’s bit “0.”

Figure 3

Phase-space picture of the original four-state protocol.

Figure 4

Phase-space picture of the three-state protocol.

Figure 5

Phase-space picture of the efficient four-state protocol.

Figure 6

Phase-space picture of the six-state protocol.

Figure 7

Phase-space picture of the eight-state protocol.

Figure 8

Phase-space picture of the $4n+4$-state protocol.

Figure 9

Phase-space picture of the mixtures of two coherent states.