A geometric invariant in entanglement

Shahabeddin Mostafanazhad aslmarand, Warner A. Miller, Doyeol Ahn +1 more

Hoshang Heydari

We investigate entanglement dynamics and properties of double Jaynes-Cummings model. In particular we study the dynamics of double Jaynes-Cummings model based on geometric invariants for four qubits. We show that these geometric invariants provide us with useful information about different types of entanglement during the quantum evolution of the system.

Alexander A. Klyachko

The main objective of the paper is to unveil an adequate mathematics hidden behind entanglement, that is Geometric Invariant Theory. More specifically relation between these two subjects can be described by the following theses. (i) Total variance of completely entangled state is maximal. (ii) This distinguishes the state as a minimal vector in its orbit under action of complexified dynamic group. (iii) An ultimate aim of Geometric Invariant Theory is a description of complex orbits and their minimal vectors. It suggests that noncompletely entangled states are just GIT semistable vectors.

Dharmaraj Ramachandran, Radhika Vathsan

Peter J. Love, Alec Maassen van den Brink, Anatoly Yu. Smirnov +5 more

Hoshang Heydari

We construct entanglement monotones for multi-qubit states based on Plücker coordinate equations of Grassmann variety, which are a central notion in geometric invariant theory. As an illustrative example, we in detail investigate entanglement monotones of a three-qubit state.