Programmable discriminator of coherent states: Experimental realization

An optical implementation of the recently proposed unambiguous identification of coherent states is presented. Our system works as a programmable discriminator between two, in general nonorthogonal, weak coherent states. The principle of operation lies in the interference of three light beams–two program states and one unknown coherent state which can be equal to either one of the two program states. The experiment is based on fiber optics. Its results confirm theoretical predictions, and the experimental setup can be straightforwardly extended for higher numbers of program states.

Figure 1

The scheme of our experimental setup. $A$, attenuator; PM, phase modulator; AG, adjustable air gap; BS, beam splitter; $D$, detector.

Figure 2

(Color online) Dependence of the fraction of correct and erroneous results on the phase difference between states $|{\alpha }_1⟩$ and $|{\alpha }_2⟩$ for three different intensities of states; ${\left|{\alpha }_1\right|}^2={\left|{\alpha }_2\right|}^2$. Solid lines represent theoretical predictions for the probability of a conclusive result.

Figure 3

(Color online) Dependence of the fraction of correct and erroneous results on the phase difference between states $|{\alpha }_1⟩$ and $|{\alpha }_2⟩$; ${\left|{\alpha }_1\right|}^2\ne {\left|{\alpha }_2\right|}^2$. Solid line represents a theoretical prediction for the probability of a conclusive result.

Figure 4

(Color online) Dependence of the probability of a conclusive result on the intensity of states (${\left|{\alpha }_1\right|}^2={\left|{\alpha }_2\right|}^2$; phase difference between states 180°). Solid line represents the theoretical prediction for our detectors with $\eta =53\%$. Dashed line is the theoretical limit for ideal detectors (quantum efficiency $\eta =100\%$).

Figure 5

(Color online) Dependence of the probability of a conclusive result on the intensity ratio of states ${\left|{\alpha }_2\right|}^2/{\left|{\alpha }_1\right|}^2$ (${\left|{\alpha }_1\right|}^2=1.33$ photons/pulse). The upper line represents the theoretical prediction for the phase difference 180° between states $|{\alpha }_1⟩$ and $|{\alpha }_2⟩$ and the lower line corresponds to the phase difference 0°.

Figure 6

Possible extension of the discrimination scheme for $N$ program states. ${\text{BS}}_0$ equally splits an unknown state into $N$ fibers. Splitting ratios of ${\text{BS}}_j$, $j=1,\dots ,N$ are $T_j=N/\left(N+1\right)$, $R_j=1/\left(N+1\right)$.