GENERIC ENTANGLED STATES AS THE su(2) PHASE STATES

Abstract

We discuss an algebraic way to construct generic entangled states of qunits based on the polar decomposition of the su (2) algebra. In particular, we show that these states can be defined as eigenstates of certain Hermitian operators.

Entanglement of qutrits

“…)ރ‬ It follows from these two statements that all entangled states of a given system can be constructed from a certain generic CE state by means of SLOCC. A simple algorithm for construction of generic entangled states has been proposed in [19].…”

“…The system is defined in the Hilbert space (5) and has the dynamic symmetry SU(3) × SU(3). The generic CE state of the system has the form [1,19]…”

Entanglement and its operational measure

“…Through the use of definition (2), one can obtain infinitely many completely entangled states ψ CE ∈ H of the same system. Among them, special attention should be paid to generic entangled states, i.e., to completely entangled states with a simple structure (like EPR and GHZ states of two and three qubits, respectively), which can be used to construct an orthonormal basis of completely entangled states in H (see [31]).…”

Generic entangled states

“…where φ k denotes a certain angle. The aim of this note is to show that generic entangled states of an arbitrary system of N qunits are the su(2) phase states of dimension n (also see Binicioglu et al 2005). Here by qunit we mean an n-state quantum system with the basic lobservables given by the orthogonal basis of the su(n) algebra.…”