Planar k-Uniform States: a Generalization of Planar Maximally Entangled States

Abstract

Recently, Doroudiani and Karimipour [Phys. Rev. A \textbf{102} 012427(2020)] proposed the notation of planar maximally entangled (PME) states which are a wider class of multipartite entangled states than absolutely maximally entangled (AME) states. There they presented their constructions in the multipartite systems but the number of particles is restricted to be even. Here we first solve the remaining cases, i.e., constructions of planar maximally entangled states on systems with odd number of particles. In addition, we generalized the PME to the planar $k$-uniform states whose reductions to any adjacent $k$ parties along a circle of $N$ parties are maximally mixed. We presented a method to construct sets of planar $k$-uniform states which have minimal support.

13pages, 3 figures, submitted to Quantum Information Processing

References in corpus (6)

• Experimental quantum teleportation
• Using entanglement against noise in quantum metrology
• Maximally multipartite entangled states
• Genuinely multipartite entangled states and orthogonal arrays
• Detecting genuine multipartite entanglement of pure states with bipartite correlations
• Constructions of $k$-uniform states from mixed orthogonal arrays