Simple and secure quantum key distribution with biphotons

The best qubit one-way quantum-key-distribution (QKD) protocol can tolerate up to 14.6% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three-level quantum system—a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating, and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. For comparison, the security of the best possible qutrit protocol of four mutually unbiased bases was also rigorously analyzed against general attacks, with a proven bound on the acceptable error rate of 21.1%.

Figure 1

(Color online) A top projection from the north pole of an orthogonal triplet basis on the $\mid 1,1⟩$ dome. The empty circles are states identical to their $180°$ opposites. Four states on this manifold are mutually unbiased to the triplet. These four states are not orthogonal between themselves.

Figure 2

(Color online) (a) The umbrella protocol: two mutually unbiased bases within the single-photon operation subspace. (b) The three rays protocol: three ray-type bases that are not perfectly mutually unbiased.

Figure 3

Key rate analysis under intercept and resend attack of a few QKD protocols. Qubit protocols are in thin lines, dotted lines for BB84, and solid lines for the 3 MUB extension. Thick lines are for qutrit protocols. Dotted, dashed, dotted-dashed, and solid lines are for the umbrella, three rays, seven rays, and four MUB, respectively.

Figure 4

Key rate analysis for a general coherent attack. Solid (dashed) lines are for calculation with (without) noise optimization. Presented results are for three qubit and two and four qutrit MUB ($3\times 2$, $2\times 3$, and $4\times 3$ respectively).