Thermalization processes induced by quantum monitoring in multi-level systems

Abstract

We study the heat statistics of an N -dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number of measurements. In this context, conditions allowing for Infinite-Temperature Thermalization (ITT), induced by the monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the non-equilibrium evolution of the system and its initial state. Exceptions to ITT take place when the observable of the intermediate measurements is commuting (or quasi-commuting) with the Hamiltonian of the system, or when the time interval between measurements is smaller or comparable with the energy scale of the quantum system (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N → ∞) -describing continuous systems with a discrete spectrum -are presented. By denoting with M the number of quantum measurements, we show that the order of the limits M → ∞ and N → ∞ matters: when N is fixed and M diverges, then there is ITT. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A non trivial result is obtained fixing M/N 2 where partial ITT occurs. Finally, an example of incomplete thermalization applicable to rotating two-dimensional gases is presented.

Experimental verification of fluctuation relations with a quantum computer

“…namely, as a consequence of the protocol applied on the qubit, the latter gets randomised into the completely mixed state ρ = 1/2. The phenomenon of randomisation induced by a train of measurements has been observed and discussed earlier, see e.g., [7,[20][21][22], but here it occurs as a consequence a different mecahnism. After preparation in a state that is diagonal in the σ z basis, the qubit undergoes a rotation of a vanishingly small angle in the large N limit.…”

“…with |n 1 n 2 and the eigenstates of the total Hamiltonian. The heat engine fluctuation relation (22) has been experimentally investigated only very recently with an NMR platform (using a quantum Otto heat engine design) by means of interferometric techniques that allow for the measurement of the characteristic function of the statistics…”