Hyper-Entanglement in Time and Frequency
Piotr Roztocki, Alfonso Carmelo Cino, Sai T. Chu, Brent E. Little, David Moss, Lucia Caspani, William J. Munro, José Azaña, Michael Kues, Roberto Morandotti, Christian Reimer, Stefania Sciara, Mehedi Islam, Luis Romero Cortés, Yanbing Zhang, Bennet Fischer, Sébastien Loranger, Raman Kashyap · 2019
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 time and frequency can be used for genuine multi-partite hyper-entangled states [2]. This is achieved by increasing the time-frequency product to far exceed the Heisenberg uncertainty limit, effectively making the time and frequency degrees independent.