Quantum Decoherence with Holography

Quantum decoherence is the loss of a system's purity due to its interaction with the surrounding environment. Via the AdS/CFT correspondence, we study how a system decoheres when its environment is a strongly-coupled theory. In the Feynman-Vernon formalism, we compute the influence functional holographically by relating it to the generating function of Schwinger-Keldysh propagators and thereby obtain the dynamics of the system's density matrix. We present two exactly solvable examples: (1) a straight string in a BTZ black hole and (2) a scalar probe in AdS$_5$. We prepare an initial state that mimics Schr\"odinger's cat and identify different stages of its decoherence process using the time-scaling behaviors of R\'enyi entropy. We also relate decoherence to local quantum quenches, and by comparing the time evolution behaviors of the Wigner function and R\'enyi entropy we demonstrate that the relaxation of local quantum excitations leads to the collapse of its wave-function.