Fractional Hadamard transform with continuous variables in the context of quantum optics

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing operators. This is extended to the entangled case by using the bipartite entangled state representation. The new transformation presents more flexibility to represent signals in the fractional Hadamard domain with extra freedom provided by an angle and two-squeezing parameters.