Direct generation of multiphoton hyperentanglement

Abstract

Multiphoton hyperentangement is fundamental in optical quantum information processing. Existing theory and experiments usually focus on producing two-photon hyperentanglement and multiphoton entangled states encoded in a single degree of freedom. Multiphoton entangled states have until now relied on the outcome postselection, a procedure where only the measurement results corresponding to the desired state are considered. Such an approach severely limits the usefulness of the resulting entangled states. We present the protocols of direct production of three- and four-photon hyperentanglement and extend the approach to an arbitrary number of photons through a straightforward cascade of spontaneous parametric down-conversion (SPDC) sources. The generated multiphoton hyperentangled states are encoded in polarization-spatial modes and polarization-time bin degrees of freedom, respectively. Numerical calculation shows that if the average photon number $\ensuremath{\mu}$ is 1, the down-conversion efficiency is $7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and the repetition frequency of the laser is ${10}^{9}$ Hz, the number of the generation of three-photon and four-photon hyperentanglement after cascading can reach about $5.78\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and $4.44\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ pairs per second, respectively. By eliminating the constraints of outcome postselection, our protocols may represent progresses for multiphoton hyperentangement generation and provide a pivotal role in future multiparty and high-capacity communication networks.