Multipartite $d-$level GHZ bases associated with generalized braid matrices

Abstract

We investigate the generalized braid relation ($d-$level $N-$body braid relation) and its application to quantum entanglement. By means of finite-dimensional representations of Heisenberg-Weyl algebra, a set of $d^N\times d^N$ unitary matrix representations satisfying the generalized braid relation can be constructed. Such generalized braid matrices can entangle $d-$level $N-$partite quantum states. Acting the generalized braid matrices on the standard basis, one can obtain a set of maximally entangled basis. Further study shows that such entangled basis can be viewed as the $d-$level $N-$partite Greenberger-Horne-Zeilinger (GHZ) basis.

5 pages

References in corpus (6)

• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Braiding transformation, entanglement swapping and Berry phase in entanglement space
• Optical Simulation of Yang-Baxter Equation
• Improved lower bounds on genuine-multipartite-entanglement concurrence
• Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
• Mutually unbiased bases and generalized Bell states

Cited by in corpus (1)

• Parameter-dependent Gaussian $(z,N)$-generalized Yang-Baxter operators