# Quantum Entanglement and Projective Ring Geometry

@article{Planat2006QuantumEA, title={Quantum Entanglement and Projective Ring Geometry}, author={Michel Planat and Metod Saniga and Maurice R. Kibler}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2006}, volume={2}, pages={066} }

The paper explores the basic geometrical properties of the observables charac- terizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum en- tanglement in such systems, we demonstrate that the 15 ◊ 15 multiplication table of the associated four-dimensional matrices exhibits a so-far-unnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of… Expand

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#### 26 Citations

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Abstract The paper deals with a particular type of a projective ring plane defined over the ring of double numbers over Galois fields, R ⊗ ( q ) ≡ GF( q ) ⊗ GF( q ) ≅ GF( q )[ x ]/( x ( x − 1)). The… Expand

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The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown… Expand

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A very particular connection between the commutation relations of the elements of the generalized Pauli group of a $d$-dimensional qudit, $d$ being a product of distinct primes, and the structure of… Expand

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This paper deals with three technical ingredients of geometry for quantum information. Firstly, we give an algorithm to obtain diagonal basis matrices for submodules of the Zd-module Z n d and we… Expand

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