| Entanglement, the most intriguing implication of quantum theory, embodies the most perfect correlations possible between two quantum systems. It underlies many important applications in quantum information processing, including quantum computing, quantum cryptography, dense coding, and teleportation. The power of these protocols is further enhanced with higher-order entanglement, realized in multi-particle and multi-dimensional systems. This thesis investigates the production and applications of pairs of photons simultaneously entangled in every degree of freedom, so-called "hyperentangled".;Using pairs of photons produced in spontaneous parametric down-conversion, we produce hyperentanglement and verify it by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and emission time. We produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. We also report the tomography of a 2x2x3x3 system, which was the largest photonic entangled system to be so characterized at the time it was reported.;Using hyperentanglement in spin (polarization) and orbital angular momentum as well as single-photon spin-orbit Bell-state analyzers, we demonstrate two quantum protocols. First, we demonstrate a dense-coding experiment with the largest reported channel capacity (1.630(6) bits), which breaks the conventional linear-optics threshold. In addition, we investigate optimal schemes for the discrimination of hyperentangled Bell states. Second, we remotely prepare and tomographically characterize single-photon two-qubit states, including spin-orbit entangled states, radially polarized, and mixed states.;Finally, we explore experimental schemes to create two novel states, "bound-entangled" and CGLMP states. The former are mixed states from which pure entanglement cannot be distilled; in particular, we consider the Smolin state, which is a mixture of hyperentangled states. The latter states present the puzzling property of violating a Bell-type inequality more strongly than would any maximally hyperentangled state. |
