Experimental Implementation of a Quantum Optical State Comparison Amplifier

We present an experimental demonstration of a practical nondeterministic quantum optical amplification scheme that employs two mature technologies, state comparison and photon subtraction, to achieve amplification of known sets of coherent states with high fidelity. The amplifier uses coherent states as a resource rather than single photons, which allows for a relatively simple light source, such as a diode laser, providing an increased rate of amplification. The amplifier is not restricted to low amplitude states. With respect to the two key parameters, fidelity and the amplified state production rate, we demonstrate significant improvements over previous experimental implementations, without the requirement of complex photonic components. Such a system may form the basis of trusted quantum repeaters in nonentanglement-based quantum communications systems with known phase alphabets, such as quantum key distribution or quantum digital signatures.

Figure 1

(a) Experimental implementation of the quantum optical state comparison amplifier and output state analyzer. The system comprises two interferometers. Each $D$ denotes a silicon single-photon detector [30]; VCSEL denotes a vertical cavity surface emitting laser and PRF the pulse repetition frequency of the laser. (b) Eight possible input coherent states.

Figure 2

(a) Experimental and fitted theoretical visibilities at the outer interferometer for $N=2$. The dotted grey curve is for the unconditioned output, the dashed orange curve for output conditioned on $D_0$ not firing, and the solid red curve for $D_0$ not firing and $D_1$ firing. Typical standard error in the measurements is $\pm 0.05$. (b)–(d) Fraction of the target state in the output and fidelity. The subfigures represent the fractions of the target state in the output of the state comparison amplifier (squares) and the fidelity of the output state to the target state $|g\alpha ⟩$ (dots) as a function of input photon number. (b) The two-state set, (c) the four-state set, and (d) the eight-state set. The ${|\alpha |}^2=0.0033$ point for the eight-state set has been omitted as the low number of overall counts renders this unreliable. In (b) the paler colored diamonds represent the partially conditioned case that considers only $D_1$ firing and ignores $D_0$ events. The standard error, shown for the correct state fraction, decays quickly with mean photon number. Standard errors for the fidelity are small: typically $\pm 0.0003$ for $N=2$, $\pm 0.0022$ for $N=4$, and $\pm 0.0013$ for $N=8$. Lines are theoretical best-fit curves based on experimental parameters.

Figure 3

The success rate of the amplifier corresponds to the gated count rate at the $D_1$ detector when $D_0$ does not fire and is shown for the two-state set as a function of input photon number. The success rates for the four- and eight-state sets follow that for $N=2$ closely. The line represents a theoretical best-fit curve based on experimental parameters. As our laser clock rate is set at 1 MHz a success rate of ${10}^5$ corresponds to an experimental success probability of 10%. Our maximum measured probability is 2.6%.