Dynamical decoupling in optical fibers: Preserving polarization qubits from birefringent dephasing

One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence, to protect photonic qubits from dephasing, by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. This technique can maintain photonic qubit coherence at high fidelity, making a step toward achieving scalable and useful quantum communication with photonic qubits.

Figure 1

Top: CPMG sequence implemented with half-wave plates in the diagonal basis along the fiber; $U_{\mathrm{free}}$ are the propagators corresponding to the free propagations through the dephasing segments. Bottom: Free propagations and $\pi$ rotations caused by the wave plates for the input qubit in the $+{45}^{\circ }$ state are shown on the Bloch sphere.

Figure 2

Decoherence function $W\left(x\right)$ without CPMG and with CPMG as a function of the distance along the fiber. Inset: $W\left(x\right)$ for CPMG with $M=2$ is shown (zoomed in) with the filter function $F\left(kL\right)=8{\sin }^4(kL/8){\sin }^2(kL/2)/{\cos }^2(kL/4)$ and $S\left(k\right)=\exp (-\frac{k^2{\sigma }_n^2}{2})$. Distance along the fiber is plotted in meters in the figure.

Figure 3

Fidelity obtained with CPMG wave plates in the optical fiber is shown with variation of the number of wave plates for different standard deviations of the randomly generated dephasing $\Delta \phi$ and fixed $L=10\mathrm{km},\langle \Delta L\rangle =10\mathrm{m},$ and ${\sigma }_{\Delta L}=3\mathrm{m}$.

Figure 4

Contour plot of the fidelity with the variations of the standard deviations of $\Delta L$ and $\Delta \phi$. Lighter regions show higher values of the fidelity. The simulation is done with fixed $L=10\mathrm{km},\langle \Delta L\rangle =10\mathrm{m}$.

Figure 5

Fidelity variation for different fiber lengths with $\langle \Delta L\rangle =10\mathrm{m},{\sigma }_{\Delta L}=3\mathrm{m},$ and ${\sigma }_{\Delta \phi }=\pm 100$ radians.