Quantum Latin squares and unitary error bases
(pp1318-1332)
Benjamin
Musto and Jamie Vicary
doi:
https://doi.org/10.26421/QIC16.15-16-4
Abstracts:
In this paper we introduce quantum Latin squares,
combinatorial quantum objects which generalize classical Latin squares,
and investigate their applications in quantum computer science. Our main
results are on applications to unitary error bases (UEBs), basic
structures in quantum information which lie at the heart of procedures
such as teleportation, dense coding and error correction. We present a
new method for constructing a UEB from a quantum Latin square equipped
with extra data. Developing construction techniques for UEBs has been a
major activity in quantum computation, with three primary methods
proposed: shift-and-multiply, Hadamard, and grouptheoretic. We show that
our new approach simultaneously generalizes the shift-andmultiply and
Hadamard methods. Furthermore, we explicitly construct a UEB using our
technique which we prove cannot be obtained from any of these existing
methods.
Key words:
Unitary error bases, quantum Latin squares, Hadamard
matrices |