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Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

Entanglement of four-qubit systems: A geometric atlas with polynomial compass II (the tame world). (English) Zbl 1357.81028

J. Math. Phys. 58, No. 2, 022201, 33 p. (2017).
Summary: [For part I see the authors, ibid. 55, No. 1, 012202, 31 p. (2014; Zbl 1294.81025)] We propose a new approach to the geometry of the four-qubit entanglement classes depending on parameters. More precisely, we use invariant theory and algebraic geometry to describe various stratifications of the Hilbert space by Stochastic Local Operations with Classical Communication (SLOCC) invariant algebraic varieties. The normal forms of the four-qubit classification of F. Verstraete et al. [Phys. Rev. A 55, No. 5, 052112, 5 p. (2002; doi:10.1103/PhysRevA.65.052112)] are interpreted as dense subsets of components of the dual variety of the set of separable states and an algorithm based on the invariants/covariants of the four-qubit quantum states is proposed to identify a state with a SLOCC equivalent normal form (up to qubits permutation).{
©2017 American Institute of Physics}

Cited in 11 Documents

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
14J81 Relationships between surfaces, higher-dimensional varieties, and physics

Citations:

Zbl 1294.81025
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Full Text: DOI arXiv

References:

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