Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback

It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming problem. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed coherent states, this bound does not reach the success probability of a minimum error measurement.

Figure 1

Dolinar-like receiver, which comprises interfering with a coherent reference light, photon counting, and feedback (or feedforward) control.

Figure 2

(a) Lower bound on the error probability of a sequential measurement for three-PSK optical coherent states with equal prior probabilities. (b) Ratio of the lower bound to the quantum limit.