Optimal circular states

Abstract In quantum optics, superpositions of coherent states, such as the Schrödinger cat states and compass states, and more generally, circular states, have attracted widespread attention due to their nice properties and significant applications. Concerning circular states, a natural question arises as what are the optimal parameters in these states for maximally achieving certain specified quantum features such as average photon number and nonclassicality. It turns out that this issue is highly nontrivial and subtle. In this work, we investigate optimal circular states for average photon number, and determine the optimal parameters by a combination of analytical and numerical methods. In particular, we establish several analytical results and also some rather detailed numerical results. We tabulate some numerical results, which may be useful in both theoretical and experimental studies of superpositions of coherent states.