Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity

TL;DR

This paper introduces two protocols for complete analysis of hyperentangled states in photons, utilizing cross-Kerr nonlinearities and linear optics, simplifying discrimination and aiding long-distance quantum communication.

Contribution

The paper proposes novel, simplified schemes for hyperentangled state analysis that reduce nonlinear requirements and improve practicality for quantum communication.

Findings

Complete discrimination of hyperentangled Bell and GHZ states achieved.

Schemes are generalized for N-photon hyperentangled GHZ states.

Reduction in nonlinear optical requirements compared to previous methods.

Abstract

We present two complete maximally hyperentangled state analysis protocols for photons entangled in the polarization and spatial-mode degrees of freedom. The first protocol is a hyperentangled Bell state analysis scheme for two photons and the second is a hyperentangled Greenberger-Horne- Zeilinger (GHZ) state analysis scheme for three photons. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely and deterministically discriminated with the aid of cross-Kerr nonlinearities and linear optics. We also generalize the schemes to unambiguously analyze the N-photon hyperentangled GHZ state. Compared with previous protocols, our schemes greatly simplify the discrimination process and reduce the requirements on nonlinearities by using the measured spatial-mode state to assist in the analysis of the polarization state. These advantages make our schemes useful for practical applications in long-distance high capacity quantum communication.