Revisiting the Dolinar receiver through multiple-copy state discrimination theory

We consider the problem of discriminating between two quantum coherent states by interpreting a single state as being a collection of several successive copies of weaker coherent states. By means of recent results on multiple-copy state discrimination, it is possible to give a reinterpretation of the Dolinar receiver and carry out a quite-straightforward analysis of its behavior. We also propose and investigate a suboptimal detection scheme derived from the Dolinar’s architecture, which is shown to slightly outperform some other near-optimal schemes available in the literature.

Figure 1

Symbol error probability in the case of equiprobable states ($q_0=q_1=1/2$). The performance of the considered detection strategies are reported and compared with the Helstrom bound, which is achievable by the optimal Dolinar receiver. Emphasis is given to the quantum-limited region corresponding to very weak coherent states.

Figure 2

Block diagram of the Dolinar receiver. The received signal with envelope $\pm \psi$ is displaced by a quantity $-u_{z\left(t\right)}$, where $z\left(t\right)\in \{0,1\}$ is the temporary estimation at time $t$. The value of $z\left(t\right)$ alternately changes from 0 to 1 at each single-photon detection of the displaced signal $\pm \psi -u_{z\left(t\right)}$. The shape of the feedback signal $u_{z\left(t\right)}$ is also changed accordingly.

Figure 3

Intensity ${\left|\beta \right|}^2$ of the fixed displacement $D(-\beta )$ for the considered receivers, with $q_0=q_1=1/2$, $T=1$.