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Quantum state teleportation of optical number states is conspicuously absentfrom the list of experimental milestones achieved to date. Here we demonstrateanalytically a teleportation scheme with fidelity $100\%$ for optical numberstates of arbitrary dimension using linear optical elements only. To this end,we develop an EPR source to supply Bell-type states for the teleportation, andshow how the same set-up can also be used as a Bell-state analyser (BSA) whenimplemented in a time-reversal manner. These two aspects are then broughttogether to complete the teleportation protocol in a scheme that can deliverperfect fidelity, albeit with an efficiency that decays exponentially as theoccupation of the number states increases stepwise. The EPR source and BSAschemes both consist of two optical axes in a symmetrical V-shape experimentallayout, along which beam-splitters are placed cross-beam fashion at regularintervals, with their transmittivities treated as variables for which thevalues are calculated ad hoc. In particular, we show the full treatment for thecase of qutrit teleportation, and calculate the transmittivity values of thebeam splitters required for teleporting qubits, qutrits, qupentits, quheptitsand qunits. The general case for arbitrary-dimensional number stateteleportation is demonstrated through a counting argument.

Arbitrary-dimensional teleportation of optical number states with linear optics