Some Possibility and Impossibility Results related to Discrete Fourier type transforms in Quantum Information

Very recently the most general ensemble of qubits are identified using the notion of linearity; any of these qubits gets accepted by a Hadamard gate to generate the equal superposition of the qubit and its orthogonal. Towards more generalization, we investigate the possibility and impossibility results related to Discrete Fourier Transform (DFT) type of operations for a more general set up of qutrits.