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Frontiers in Optics

Hyper-Entanglement: How To Enlarge Your Hilbert Space Without Really Trying

Paul G. Kwiat, Trent Graham

Published Jan 1, 2011• 1 citation
Publisher

Abstract

“Hyper-entangled” photon pairs—simultaneously entangled in multiple degrees of freedom—enable new capabilities in quantum information and metrology. We present several examples, including minimal-measurement quantum process tomography and “superdense teleportation”.
DOI
10.1364/ls.2011.ltui1

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We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyper-entangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyper-entangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported entangled system of this size to be so characterized.
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We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom and find that Bell tests beyond the standard Clauser-Horne-Shimony-Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher-dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.