Optical Information Processing with Entangled Topological States*

Topological quantities such as winding number or Chern number have become important tools for solid state physics, and more recently for photonic systems. These topological numbers are highly stable against external perturbations, which makes them attractive for encoding qubits in a robust manner. But they are difficult to determine by local measurements, especially in photonic systems, where the relevant information is often carried by a single photon that is destroyed in the measurement. Here, we use linear optical multiports as a means of constructing systems in which winding number and polarization are jointly entangled. This leads to a reduction in bit flip errors, due to the topological stability of the winding number, while the linkage to polarization simplifies the process of measuring the topological variable. This opens a new range of possible quantum information processing applications. We examine topologically-entangled bulk and boundary states, and outline several applications, such as the construction of topologically-protected photonic memory registers and of entangled memory registers.