A note on the Bloch representation of absolutely maximally entangled states

Abstract

The absolutely maximally entangled (AME) states play key roles in quantum information processing. We provide an explicit expression of the generalized Bloch representation of AME states for general dimension $d$ of individual subsystems and arbitrary number of partite $n$. Based on this analytic formula, we prove that the trace of the squared support for any given weight is given by the so-called hyper-geometric function and is irrelevant with the choices of the subsystems. The optimal point for the existence of AME states is obtained.

References in corpus (7)

• Multi-party entanglement in graph states
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution
• Genuinely multipartite entangled states and orthogonal arrays
• All Maximally Entangled Four Qubits States
• Exploring pure quantum states with maximally mixed reductions
• Holographic codes