Experimental Implementation of the Optimal Linear-Optical Controlled Phase Gate

We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of postselected linear-optical implementations with vacuum ancillas. The quantum gate is implemented by using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the optimum success probability is not monotone in the phase.

Figure 1

Conceptual scheme of the gate. Vertically ($V$) and horizontally ($H$) polarized components of the same beam are drawn separately for clarity. In polarization beam splitters PBS1 and PBS2 the vertical components are reflected. Half-wave plates $\mathrm{HWP}b$ and $\mathrm{HWP}c$ act as “beam splitters” for $V$ and $H$ polarization modes. F1 and F2 are filters (attenuators); F1 acts on the both polarization modes, F2 on the $H$ component only. Phase shifts ${\varphi }_{+}$ and ${\varphi }_{-}$ are introduced by proper path differences in the respective modes. $\mathrm{HWP}a$ and $\mathrm{HWP}d$ just swap vertical and horizontal polarizations. In the final setup they are omitted for simplicity, and the second qubit is encoded inversely with respect to the first qubit.

Figure 2

Scheme of the actual experimental setup (see the text and Ref. 17 for details).

Figure 3

Choi matrices for the gate with $\phi =\pi /2$. The left top panel shows the real part of the reconstructed process matrix, while the left bottom one displays its imaginary part. The process fidelity $F_{\chi }=86\%$. The two right panels show the ideal matrix.

Figure 4

Success probability of the gate.