A note on Majorana representation of quantum states

We study the Majorana representation of quantum states using symmetry class of tensors. We present a simple method to construct $d-1$ points on the Bloch sphere and their corresponding $d-1$ qubits, effectively representing a $d$-dimensional quantum state. Additionally, we demonstrate how the inner product of two $d$-dimensional quantum states can be expressed as a permanent of a matrix related to their $(d-1)$-qubit state representations. Furthermore, we discuss the implications of this result on the convexity of a specific decomposable numerical range.