Generation of Hyperentangled Photon Pairs

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, 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 hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a $2\times 2\times 3\times 3$ system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.

Figure 1

Experimental setup for the creation and analysis of hyperentangled photons. (a) The photons, produced using adjacent nonlinear crystals (BBO), pass through a state filtration process for each DOF before coincidence detection. The measurement insets show the filtration processes as a transformation of the target state (dashed box) and a filtering step to discard the other components of the state (dotted box). (b) Spatial filtration (spa): hologram (holo) and single-mode fiber (smf). (c) Energy-time transformation (e-t): thick quartz decoherer (dec) and liquid crystal (LC). (d) Polarization filtration (poln): quarter-wave plate (qwp), half-wave plate (hwp), and polarizer (pol).

Figure 2

Measured density matrix ($\rho$) and close pure state [$|{\Psi }_p⟩\sim {\Phi }_{\mathrm{poln}}^{+}\otimes (|lr⟩+\alpha |gg⟩+|rl⟩)$ with $\alpha =1.88e^{0.16i\pi }$] of a ($2\times 2\times 3\times 3$)-dimensional state of 2-photon polarization and spatial mode [35].

Figure 3

Measured density matrices (real parts) of ($2\times 2\times 2\times 2$)-dimensional states of 2-photon polarization and ($+1,-1$)-qubit OAM [35]. For each state, we list the target state ${\rho }_t$, the fidelity $F(\rho ,{\rho }_t)$ of the measured state $\rho$ with the target ${\rho }_t$, their negativities and linear entropies, and the tangle and linear entropy for each subspace. The negativity for two-qubit states is the square root of the tangle. The magnitudes of all imaginary elements, not shown, are less than 0.03.