Explicit constructions of three quantum Latin squares of order 6 achieving cardinalities 13, 15, and 17 via orthogonal decompositions and Hadamard pairs.
Quantum Latin squares and unitary error bases
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abstract
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 algebraic. 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.
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This review compiles fourteen equivalent formulations of the open existence problem for maximal mutually unbiased bases in composite dimensions and summarizes known analytic, computer-aided and numerical results along with potential solution strategies.
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Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17
Explicit constructions of three quantum Latin squares of order 6 achieving cardinalities 13, 15, and 17 via orthogonal decompositions and Hadamard pairs.
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Mutually Unbiased Bases in Composite Dimensions -- A Review
This review compiles fourteen equivalent formulations of the open existence problem for maximal mutually unbiased bases in composite dimensions and summarizes known analytic, computer-aided and numerical results along with potential solution strategies.