Quantum Communication without Alignment using Multiple-Qubit Single-Photon States

We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell’s inequalities, quantum dense coding, and quantum teleportation.

Figure 1

Polarization and HG modes of the electromagnetic field. Top: horizontal polarization $|H⟩$ and ${\mathrm{HG}}_{01}$ mode $|h⟩$ (left), vertical polarization $|V⟩$ and ${\mathrm{HG}}_{10}$ mode $|v⟩$ (right). Center: diagonal polarizations $(|H⟩\pm |V⟩)/\sqrt{2}$ and diagonal modes $(|h⟩\pm |v⟩)/\sqrt{2}$. Bottom: circular polarizations $(|H⟩\pm i|V⟩)/\sqrt{2}$ and circular modes $(|h⟩\pm i|v⟩)/\sqrt{2}$.

Figure 2

Bell-state measurement device for logical qubits using a 50-50 beam splitter (BS). MS is a transverse mode sorter and PBS a polarizing beam splitter.