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2016

Exploring quantum teleportation through unitary error bases

Musto, Benjamin

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Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction.

Werner's combinatorial construction builds a unitary error basis from a family of Hadamard matrices and a Latin square.
In this dissertation, I give a new categorical axiomatisation of Latin squares, and use this to give a fully graphical presentation and proof of the correctness of Werner's construction.
The categorical approach makes clear that some of the Latin square axioms are unnecessary for the construction to go through, and I propose a generalised construction scheme with the potential to create new classes of unitary error bases.

Exploring quantum teleportation through unitary error bases · Around

Built on

The 6 × \times 6 latin squares
Ronald Aylmer Fisher and Frank Yates · 1934
Earlier work this paper cites.
Quasigroups. i
Adrian A Albert · 1943
Earlier work this paper cites.
Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels
Charles H Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K Wootters · 1993
Earlier work this paper cites.
Group representations, error bases and quantum codes
Emanuel Knill · 1996
Earlier work this paper cites.

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