“…Nevertheless, to teleport quantum states of a real particle, such as a single photon, one needs to consider not only the two-level states (polarization), but also those multi-level states [25,38,50]. For example, the orbital angular momentum [16,37], the temporal mode [3,42], the frequency mode [30], and the spatial mode [24,45] of a single photon are all natural attributes of multi-level states, which are exploited as high-dimensional systems. It is worth mentioning that ref [22] has made an argument that as the dimension of the constituent qudits increases, the cost of maintaining a qudit in a fully entangled state also increases and the optimum cost per Hilbert dimension is attained at the local dimension of d = 3 (d is the dimensionality of Hilbert space).…”