Superselection Rules and Bosonic Quantum Computational Resources

We present a method to systematically identify and classify quantum optical nonclassical states as classical or nonclassical based on the resources they create on a bosonic quantum computer. This is achieved by converting arbitrary bosonic states into multiple modes, each occupied by a single photon, thereby defining qubits of a bosonic quantum computer. Starting from a bosonic classical-like state in a representation that explicitly respects particle number superselection rules, we apply universal gates to create arbitrary superpositions of states with the same total particle number. The nonclassicality of the corresponding states can then be associated with the operations they induce in the quantum computer. We also provide a correspondence between the adopted representation and the more conventional one in quantum optics, where superpositions of Fock states describe quantum optical states, and we identify how multimode states can lead to quantum advantage. Our work contributes to establish a seamless transition from continuous to discrete properties of quantum optics while laying the grounds for a description of nonclassicality and quantum computational advantage that is applicable to spin systems as well.