Quantum Latin squares and unitary error bases

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • University of Oxford


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 group-theoretic. We show that our new approach simultaneously generalizes the shift-and-multiply and Hadamard methods. Furthermore, we explicitly construct a UEB using our technique which we prove cannot be obtained from any of these existing methods.


Original languageEnglish
Pages (from-to)1318-1332
JournalQuantum Information and Computation
Issue number15-16
Publication statusPublished - 1 Nov 2016