3,250 research outputs found
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares
Difference arrays are used in applications such as software testing,
authentication codes and data compression. Pseudo-orthogonal Latin squares are
used in experimental designs. A special class of pseudo-orthogonal Latin
squares are the mutually nearly orthogonal Latin squares (MNOLS) first
discussed in 2002, with general constructions given in 2007. In this paper we
develop row complete MNOLS from difference covering arrays. We will use this
connection to settle the spectrum question for sets of 3 mutually
pseudo-orthogonal Latin squares of even order, for all but the order 146
Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
Absolutely Maximally Entangled (AME) states are those multipartite quantum
states that carry absolute maximum entanglement in all possible partitions. AME
states are known to play a relevant role in multipartite teleportation, in
quantum secret sharing and they provide the basis novel tensor networks related
to holography. We present alternative constructions of AME states and show
their link with combinatorial designs. We also analyze a key property of AME,
namely their relation to tensors that can be understood as unitary
transformations in every of its bi-partitions. We call this property
multi-unitarity.Comment: 18 pages, 2 figures. Comments are very welcom
Mutually unbiased bases and discrete Wigner functions
Mutually unbiased bases and discrete Wigner functions are closely, but not
uniquely related. Such a connection becomes more interesting when the Hilbert
space has a dimension that is a power of a prime , which describes a
composite system of qudits. Hence, entanglement naturally enters the
picture. Although our results are general, we concentrate on the simplest
nontrivial example of dimension . It is shown that the number of
fundamentally different Wigner functions is severely limited if one
simultaneously imposes translational covariance and that the generating
operators consist of rotations around two orthogonal axes, acting on the
individual qubits only.Comment: 9 pages, 6 tables, 6 figures. Accepted for publication in J. Opt.
Soc. Am. B, special issue on Optical Quantum Information Scienc
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