On the geometry of a class of N-qubit entanglement monotones

Abstract

A family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the three-tangle, and some of the four, five and N-qubit SLOCC invariants introduced recently. The construction of these invariants is based on bipartite partitions of the Hilbert space in the form ${\mathbf{C}}^{2^N}\simeq {\mathbf{C}}^L\otimes {\mathbf{C}}^l$ with $L=2^{N-n}\ge l=2^n$. Such partitions can be given a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes in ${\mathbf{C}}^L$ that can be realized as the zero locus of quadratic polinomials in the complex projective space of suitable dimension via the Plucker embedding. The invariants are neatly expressed in terms of the Plucker coordinates of the Grassmannian.

7 pages RevTex, Submitted to Physical Review A

Cited by in corpus (13)

• Black Holes, Qubits and Octonions
• On polynomial invariants of several qubits
• Stringy Black Holes and the Geometry of Entanglement
• On the geometry of four qubit invariants
• Geometric phases and Bloch sphere constructions for SU(N), with a complete description of SU(4)
• Qubits and oriented matroids in four time and four space dimensions
• Phirotopes, Super p-branes and Qubit Theory
• Local Unitary Invariants for N-qubit Pure State
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Dirac Equation in Four Time and Four Space Dimensions
• Geometric multipartite entanglement measures
• Generalized Elko Theory
• Some Mathematical and Physical Remarks on Surreal Numbers