Recent advances in experimental technique make SuperDense Teleportation (SDT) possible only now, ten years after my first proposal at an ISI Torino summer conference on Quantum Computing. The effect uses remote state preparation to send more state-specifying parameters per bit than ordinary quantum teleportation (QT) can transmit. The SDT uses a maximally entangled state to teleport the relative phases of an n-dimensional state with equal amplitudes on every standard basis vector. For n greater than or equal to 3, the SDT sends more of these state-specifying parameters than QT. In the limit of large n the ratio is 2 to 1, hence the nomenclature by analogy with Super Dense Coding. Alice’s measurements and Bob’s transformations are far simpler than their corresponding operations in QT. The roles of Charles who chooses the state and Diana who deploys it are different than in QT. My discussion includes a brief review of the progress and possibilities of realization for several different experimental approaches around the world. This paper is the write-up of my remarks at the Festschrift conference for Anton Zeilinger, for many years a close collaborator in the Hampshire College NSF grant continuing our work with Mike Horne and Danny Greenberger started under Cliff Shull at MIT in the late 20th century.
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Note that this is true in any dimension – perfect entanglement is not needed. And this suggests a method for teleporting states with arbitrary amplitudes and phases; that possibility is the subject of another investigation [Bernstein 2005, in process].
In fact one can choose to make a single phase into a relative amplitude variable, by simple coordinate transformation, in any number of dimensions. But the topological difference between N-dimensional complex hyper-spherical space of a full quNit (a singular projective space) and the simpler hyper-torus to which the SuperDense process is restricted prevents teleportation of more than one relative amplitude. The relative amplitude that is teleported can only be between components of the state vector chosen by Charles to be relatively real.
H. J. Bernstein, unpublished talk, ISI Torino Summer Conference on Quantum Computation (1996).
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Bernstein, H.J. SuperDense Quantum Teleportation. Quantum Inf Process 5, 451–461 (2006). https://doi.org/10.1007/s11128-006-0030-5
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DOI: https://doi.org/10.1007/s11128-006-0030-5