Figure 1

(a) Principal scheme for teleportation of three-dimensional quantum states. Alice holds a quantum state | φ a ⟩ encoded in three dimensions (depicted by three paths) that she wishes to teleport to Bob. To do so, they first share a three-dimensional, maximally entangled state. Then Alice performs a high-dimensional Bell-state measurement (HD BSM) on her photons. Conceptually, our approach upon realizing a HD BSM consists of two parts: a unitary transformation in an expanded state space ( U ˜ 3 + 1 ) and a multiport beam splitter that enables collective quantum interference between Alice’s teleportee photon ( a ), her part of the entangled state ( b ), and an additional ancillary photon ( x ). Specific click patterns of different detectors indicate successful projections into one of the nine entangled Bell states. Alice can now transmit the classical information of her click pattern to Bob, who performs a unitary transformation ( U 3 ) on his photon to recover the original state of Alice’s teleportee photon. (b) Experimental setup to teleport path-encoded qutrits. An ultraviolet pulsed laser is used to create a three-dimensionally entangled photon pair (path-encoded) in a nonlinear crystal ( BBO 1 ) shared between Alice and Bob. The teleportee and ancillary photon are produced in a second nonlinear crystal ( BBO 2 ). All 12 input qutrit states to be teleported and the ancilla photon are prepared using polarization-dependent beam displacers (BDs) controlled by half- and quarter-waver plates (HWP and QWP). The expanded unitary transformation U ˜ 3 + 1 is implemented in a four-dimensional hybrid polarization-path state space. A polarizing beam splitter (PBS) traces out the additionally employed fourth dimension. All three photons ( a , b , x ) enter the three-dimensional multiport beam splitter, which consists of nested interferometers implemented in polarization and path d.o.f. A specifically designed partially polarizing beam splitter (PPDBS) ensures equally distributed input ports to all output ports. Simultaneous click-patterns of detectors { a 0 ′ , a 1 ′ , a 2 ′ } , { b 0 ′ , b 1 ′ , b 2 ′ } , or { x 0 ′ , x 1 ′ , x 2 ′ } indicate a successful BSM and herald a teleported photon at Bob’s side. No active feed-forward scheme was implemented here. Adjusting the HWP and QWP in Bob’s measurement apparatus allows for a complete analysis of the teleported qutrits.