Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement

We present a technique for hyperentangled Bell-state analysis that only relies on linear optics and is assisted by auxiliary entangled states. This technique can be used to implement hyperdense coding with an experimentally realizable two-photon state hyperentangled in polarization and two longitudinal-momentum degrees of freedom. The 16 hyperentangled states in the first two degrees of freedom are classified into 12 groups with the help of the third degree of freedom. This allows the transmission of 3.58 bits/photon via our hyperdense coding scheme. We also generalize our technique to $n$-qubit hyperentangled Bell-state analysis assisted by additional auxiliary entangled states. We show that given $n$ degrees of freedom, the $4^n$ hyperentangled Bell states can be separated via linear optics into $x_k=2^{n+k+1}-2^{2k}$ groups with the help of $k(k\le n)$ ancillary entangled states. When $k=n$, all $4^n$ hyperentangled states can be distinguished. Our results are useful for quantum information processing based on hyperentanglement.

Figure 1

Schematic of the setup for HBSA of two DOFs when photons are entangled in three DOF.