Noise induced regression to classical dynamics in the single mode Kerr Effect

Quantum information processing devices promise speed-ups in certain tasks over their classical counterparts, especially as the system size grows. However, it is well known that a quantum system undergoing decoherence regresses to its classical counterpart as time progresses, and does so more rapidly as the system becomes more macroscopic. Progress in the Noisy Intermediate Scale Quantum (NISQ) computing era motivates us to better understand this transition in a quantitative way. We quantify the quantum-to-classical transition of single mode Kerr Hamiltonian in the presence of noise. We study the interplay of the generation of coherence and the degradation of this coherence with the increasing system size. It is shown that, as we increase the system size, the generation of so-called kitten states is severely restricted even in the presence of modest photon-loss. We show that the expectation values of observables coincide with the classical expectation values in this regime. Given that the generation of kitten states is severely restricted, we further ask, is there any "quantumness" generated in the system at early times by studying the early time behavior based on a mean-field approximation. Our results quantify the effect of noise on the quantum resources generated in the system and cast doubt on the effectiveness of NISQ devices.