Measurement Induced Phase Transition in the Central Spin Model: Second Rényi Entropy Approach

This paper studies the dynamics of the phase transition induced by measurements in the central spin model using a second entropy Renyi approach. The study contributes to the theoretical understanding of dynamical phase transitions in quantum systems that are subject to continuous random measurements. In this work, using a new method based on the use of Renyi second entropy in dual space, we have been able to quantify the critical measurement rates and show that they are very different from those predicted by the simple mutual entropy approach. In addition, our simulation results show how decoherence, energy relaxation and quantum gate errors affect the existence of the phase transition, with meaningful implications for experimental realisation. The work opens new perspectives for the use of measurement-induced phase transitions in the field of noise-tolerant algorithms.