Demonstration of a quantum error correction for enhanced sensitivity of photonic measurements

The sensitivity of classical and quantum sensing is impaired in a noisy environment. Thus, one of the main challenges facing sensing protocols is to reduce the noise while preserving the signal. State-of-the-art quantum sensing protocols that rely on dynamical decoupling achieve this goal under the restriction of long noise correlation times. We implement a proof-of-principle experiment of a protocol to recover sensitivity by using an error correction for photonic systems that does not have this restriction. The protocol uses a protected entangled qubit to correct a single error. Our results show a recovery of about $87\%$ of the sensitivity, independent of the noise probability.

Figure 1

The experimental setup. The 780-nm entangled photons are generated by a noncollinear type-II parametric downconversion from 2-mm-thick $\beta -{\mathrm{BaB}}_2{\mathrm{O}}_4$ (BBO) crystal using a 390-nm doubled Ti:sapphire pulsed laser [37]. One photon measures a birefringence phase ($\theta$ in the figure), generated by two 2-mm tilted calcite crystals with perpendicular optical axes [36]. The bit flip is generated by a ${45}^{\circ }$ half-wave plate (HWP) for the horizontal polarization (sad face in the figure). The error correction is composed of two quarter-wave plates (QWPs) placed in the two paths and a $22.5^{\circ }$ HWP in the noisy path. A PBS completes the error correction protocol. The multiple phase accumulation part is implemented by a 31.5-m-long delay line, projecting photons from different pulses [39]. Two $22.5^{\circ }$ HWPs are placed before the projecting PBS to avoid the collapse of the state by the measurement of the first photon. The block of the projecting PBS and the HWPs was not used, as the results in this work were taken without the multiple phase accumulation part. Eventually, basis transformation is carried out with HWPs and QWPs, and the photons are detected by single-photon detectors. The data are accumulated by FPGA electronics.

Figure 2

The visibility $V_{RL}$ as a function of the phase. Solid and open symbols denote perturbed and unperturbed states, respectively. Circles and boxes denote corrected and uncorrected states, respectively. Solid lines represent fits to sine functions. The corrected states have the same phase as the original state, while the perturbed uncorrected state has an opposite phase. Errors were calculated assuming Poisson error distributions. They are smaller than the symbol sizes, and thus, they are not displayed.

Figure 3

The sensitivity as a function of the noise probability, with an error correction (solid blue circles) and without (empty green boxes). Errors were calculated assuming Poisson error distributions. They are smaller than the symbol sizes, and thus, they are not displayed.

Figure 4

The fidelity with the original state as a function of the phase. The notations and colors are the same as in Fig. 2. Errors were calculated assuming Poisson error distributions.