Squeezed-State Purification with Linear Optics and Feedforward

A scheme for optimal and deterministic linear optical purification of mixed squeezed Gaussian states is proposed and experimentally demonstrated. The scheme requires only linear optical elements and homodyne detectors, and allows the balance between purification efficacy and squeezing degradation to be controlled. One particular choice of parameters gave a tenfold reduction of the thermal noise with a corresponding squeezing degradation of only 11%. We prove optimality of the protocol, and show that it can be used to enhance the performance of quantum informational protocols such as dense coding and entanglement generation.

Figure 1

Experimental setup of the phase noise subtraction scheme. A fraction of input mode $\widehat{a}$ is tapped off to perform phase quadrature measurements using interferometer I. The resulting photocurrent is amplified (AMP) and, after introducing an appropriate cable delay, fed forward to the modulator. The amplitude and phase noise of the transmitted mode is characterized by interferometer II. AMP: electrical amplifier, PBS: polarizing beam splitter, $\lambda /2$: half-wave plate.

Figure 2

Experimental results as a function of transmission. (a) and (b) Phase and amplitude quadrature variances of the transmitted beam. (c) Product of phase and amplitude quadrature variances. Open circles and filled squares represent the results with and without feedforward, respectively; open diamonds in (a) represent values taken at reduced detection efficiency (cf. main text). Also plotted is the degree of excess noise reduction which is independent of the actual detection efficiency. The lines are obtained from our theoretical model, with the dashed line in (a) taking into account nonunit phase quadrature measurement efficiency of mode $\widehat{r}$. All variances were normalized to the shot noise level. Measurement frequency: 20.5 MHz. Electronic noise of $-83.3\mathrm{dBm}$, was subtracted from the measured data.

Figure 3

Photon number diagram showing experimental purification results and ideal purification trajectories. (a) Ideal trajectory for initial state used in experiments. (b) Trajectory for initial state with ${\Delta }^2{\widehat{X}}_{\mathrm{sqz}}=0.3$ and ${\Delta }^2{\widehat{Y}}_{\mathrm{anti}}=400$. Dark trajectories/points: no feedforward. Light trajectories/points: feedforward. The contours represent lines of constant $C_{\mathrm{EPR}}$ for $⟨\widehat{n}{⟩}_{\mathrm{cp}}=400$, normalized to $C_{\mathrm{Holevo}}$. Shading indicates the region in which dense coding is successful.