Complete hyperentangled-Bell-state analysis for quantum communication

TLDR

Unambiguous discrimination of the four polarization Bell states cannot be achieved with linear optics alone; hyperentanglement in multiple degrees of freedom has been employed to aid this task, but when the extra degree is qubitlike only seven of the sixteen hyperentangled states can be distinguished. We propose using cross‑Kerr nonlinearity to achieve complete discrimination of hyperentangled Bell states. The cross‑Kerr based scheme also supports teleportation of a particle in two degrees of freedom and entanglement swapping of hyperentangled states. The proposed protocol enhances channel capacity for long‑distance quantum communication.

Abstract

It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has been used to assist in the complete Bell-state analysis of the four Bell states. However, if the additional degree of freedom is qubitlike, one can only distinguish 7 from the group of 16 states. Here we present a way to distinguish the hyperentangled Bell states completely with the help of cross-Kerr nonlinearity. Also, we discuss its application in the quantum teleportation of a particle in an unknown state in two different degrees of freedom and in the entanglement swapping of hyperentangled states. These applications will increase the channel capacity of long-distance quantum communication.