Hyper-Entanglement in Time and Frequency

Hyper-entanglement, i.e. entanglement in more than one degree of freedom, enables a multiplicative increase in Hilbert space size. Such systems can be treated as multi-partite even though the number of state particles is not increased, making them highly attractive for applications in high-capacity quantum communications and information processing [1]. Until now, such states have been realized only using combinations of fully independent degrees of freedom, described by commuting operators, such as polarization and optical paths. Time and frequency, in turn, are linked and described by non-commuting operators. Here, using two discrete forms of energy-time entanglement we demonstrate that ti…