Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis

We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-z gate. This new architecture is ideally suited to guided optics implementations of optical gates.

Figure 1

(a) Interferometric CZ gate based on the approach of Refs. 13, 14. Gate operation is enabled by transforming each qubit from polarization to spatial encoding and back again. This requires high interferometric stability and spatiotemporal mode matching for correct operation. (b) Partially polarizing beam splitter gate. The qubits can remain polarization encoded, since the vertically polarized modes are completely reflected by the first PPBS and do not interact. Nonclassical interference occurs between the horizontally polarized modes, with $\eta =1/3$. The subsequent PPBSs give the required losses in the $c_V$ and $t_V$ modes as shown in (a).

Figure 2

Quantum process tomography of the CZ gate. Real components of the $\chi$ matrix for the: (a) ideal, (b) cw, and (c) pulsed CZ gates. The imaginary components of the experimental matrices are not shown: A few elements are on the order of 0.05; the average is $\sim 0.005$.

Figure 3

The CZ gate operating as a Bell-state analyzer. (a) The two-qubit entangled state at the output of the fibers and (b) transformed to the ${\varphi }^{+}$ Bell state. (c) The measured truth table: The average probability of success is $0.78\pm 0.03$. (d)–(g) Transformation of near-maximally entangled states to near-separable states by a CZ gate Bell-state analyzer. (d) The input Bell states determined from (e) the measured input states with the second qubit rotated by a Hadamard. (f) The measured output states, (g) transformed by applying local rotations to each qubit (see text).