A Concise Guide to Complex Hadamard Matrices

By Wojciech Tadej, Karol Zyczkowski. Open systems & information dynamics, 2005

320 citations recorded by the source corpus.

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12,14 and 16, which we could not find in the existing literature.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/835ecff83b26a9a9ed0226e8fc19154490845976

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

1. Ferenc SzollHosi
2. Dardo Goyeneche
3. Karol Zyczkowski
4. Wojciech Tadej
5. Ingemar Bengtsson

Citations in the corpus

• Genuinely multipartite entangled states and orthogonal arrays (2014, methodology): “Extend Theorem 9 to the case of 2–uniform states of qudits by using Butson–type complex Hadamard matrices [58].”
• Defect of a unitary matrix (2007, methodology): “For a composite N the defect of FN is positive, and it is usually greater than the dimension of affine Hadamard families stemming from FN , introduced in [15].”
• Interacting quantum observables: categorical algebra and diagrammatics (2009, background): “If d = 2, 3 or 5 the only dephased Hadamards are Fourier matrices [42], hence we can conclude that every pair of coherent COSs in these dimensions is closed.”
• Geometry of Quantum States: Index (2007, background): “10 For complex Hadamard matrices in general, see Tadej and Życzkowski [883], and Szöllősi [880].”
• Construction, classification and parametrization of complex Hadamard matrices (2011, methodology): “Note that F (5) 8 (aτ, bτ (2), cτ (3), dτ (2), eτ (3)) where τ = e is an eighth root of unity coincides with the matrix listed in [138], and hence is of Diţă-type.”