Superselection rules and bosonic quantum computational resources

TL;DR

This paper introduces a systematic method to classify quantum optical states as classical or non-classical based on their computational resources, linking super-selection rules to quantum advantage in bosonic systems.

Contribution

It develops a framework to identify non-classical states via particle number super-selection rules and their induced operations in bosonic quantum computing.

Findings

States with certain superpositions enable quantum advantage.

A correspondence between optical and bosonic representations is established.

The method bridges continuous and discrete quantum properties.

Abstract

We present a method to systematically identify and classify quantum optical non-classical states as classical/non-classical 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 super-selection rules, we apply universal gates to create arbitrary superpositions of states with the same total particle number. The non-classicality of the corresponding states can then be associated to 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 multi-mode 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 non-classicality and quantum computational advantage that is applicable to spin systems as well.