Experimental Nonlinear Sign Shift for Linear Optics Quantum Computation

We have realized the nonlinear sign shift operation for photonic qubits. This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift is $(1.05\pm 0.06)\pi$ in clear agreement with theory. Our results show that, by using an ancilla photon and conditional detection, nonlinear optical effects can be implemented using only linear optical elements. This experiment represents an essential step for linear optical implementations of scalable quantum computation.

Figure 1

(a) Schematic of a simplified version of NS operation constructed by a nonpolarizing beam splitter of reflectivity $R$. $|{\Psi }_{\mathrm{I}\mathrm{N}}⟩$ and $|{\Psi }_{\mathrm{O}\mathrm{U}\mathrm{T}}⟩$ are the quantum states of input and output photons. The operation is successful when the single-photon detector in ancilla mode 4 counts a single photon. (b) The two paths that lead to the detection of exactly one photon in output mode 4. As long as all of the photons are indistinguishable, these two paths can interfere.

Figure 2

Experimental setup for the demonstration of NS operation using double-pass parametric down-conversion. Photon pairs created from first pass are used for the input of NS operation and pairs from the second pass are used for the triggered single photon source as ancilla. Successful operation is identified through fourfold coincidence counts between all four detectors.

Figure 3

(a) The fourfold coincidences as a function of the pump delay mirror position for the photon-number entangled photons. HWP2 is set to rotate the polarization state by $45°$. Solid squares (circles) show the fourfold coincidence counts for the input state where $\theta =0(\pi )$. The peak and dip of the two curves are different in size only because of accidental coincidences occurring when the delay is much larger than the photons’ coherence length. (b) The fourfold coincidences as functions of the pump delay mirror position for the input photons in the state $|1_{\mathrm{V}};1_{\mathrm{H}}{⟩}_3$. The HWP2 is set to leave the input polarization states unchanged. At zero delay, the coincidences are suppressed nearly to zero by the HOM effect.

Figure 4

The observed variation of the coincidence count rates as functions of the phase of entangled photons $\theta$ at zero delay for the photon-number entangled photons. Solid triangles represent the twofold coincidences with $D_A{D}_B$ and show the phase of input photons. Solid diamonds represent the fourfold coincidences with $D_1{D}_2{D}_A{D}_B$ which show the phase of the output photons demonstrating a successful NS operation. Error bars are based on the usual Poisson fluctuation in the number of counts on the uncorrected data (error bars of twofold coincidences are too small to display). The phase of fourfold coincidence is shifted $(1.05\pm 0.06)\pi$ against twofold coincidence in agreement with the expected $\pi$ phase shift.