Demonstration of a Quantum Nondemolition Sum Gate

The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light modes. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U. L. Andersen [Phys. Rev. A 71, 042308 (2005)], solely based on off-line squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying the criteria for QND measurements in both conjugate quadratures.

Figure 1

Schematic of the experimental setup. The parameter $R$ determines the reflectivities of the four beam splitters, which are $R/(1+R)$, $R$, $R$, and $1/(1+R)$. We employ optical parametric oscillators (OPO) to produce squeezed vacuum modes, local oscillators (LO) for homodyne detection, and electro-optic modulators (EOM) combined with beam splitters ($99:1$) for signal displacement.

Figure 2

Variances of the quadrature components corresponding to vacuum inputs and $G=1.0$. Shown are the experimental QND output variances (red) with their theoretical values (pink), compared to the results with vacuum-state ancillas (green) and their theoretical values (light green). The yellow lines refer to the theoretical results for infinite squeezing, and the blue traces show the shot noise level corresponding to the variances of the input states.

Figure 3

Second moments of the quadrature components of the input and output states with respect to four different input states, for $G=1.0$. The excited input quadratures are shown in blue (nonexcited input quadratures with variances equal to the shot noise level are not shown). The output quadratures are shown in red, and, for comparison, we add the traces in green which are the output quadratures without coherent excitation.

Figure 4

Noise correlations between output quadratures, determining the conditional variances and verifying entanglement. (a) Experimental setup. The measured probe quadrature is rescaled with a variable gain $g$, added (subtracted) ($\pm$) to (from) the signal quadrature detector output, and analyzed with an electronic spectrum analyzer. Variances of ${\widehat{x}}_1^{\mathrm{out}}-g{\widehat{x}}_2^{\mathrm{out}}$ and of ${\widehat{p}}_2^{\mathrm{out}}+g{\widehat{p}}_1^{\mathrm{out}}$ are shown in (b) and (c), respectively: theoretical prediction for an ideal QND interaction (i), a QND interaction with finite degrees of squeezing of the ancilla modes (ii), and with vacuum ancilla modes (iii). By entering the areas below the lines (iv) entanglement is verified. The vertical axes are variances normalized to the shot noise power of the signal variable.