The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator
N with finite spectrum is analysed in detail. The Hamiltonian generating the time evolution of the system in the absence of direct measurements is assumed to be given by the sum of a term commuting with
N and a small perturbation not commuting with
N. The system is subject to repeated direct (projective) measurements using a single instrument whose action on the state of the system commutes with
N. If the Hamiltonian commutes with the observable
N (i.e., if the perturbation vanishes) the state of the system approaches an eigenstate of
N, as the number of direct measurements tends to
∞. If the perturbation term in the Hamiltonian does \textit{not} commute with
N the system exhibits "jumps" between different eigenstates of
N. We determine the rate of these jumps to leading order in the strength of the perturbation and show that if time is re-scaled appropriately a maximum likelihood estimate of
N approaches a Markovian jump process on the spectrum of
N, as the strength of the perturbation tends to
0.
Abstract On a quantum superconducting processor we observe partial and infinite-temperature thermalization induced by a sequence of repeated quantum projective measurements, interspersed by a unitary (Hamiltonian) evolution. Specifically, on a qubit and two-qubit systems, we test the state convergence of a monitored quantum system in the limit of a large number of quantum measurements, depending on the non-commutativity of the Hamiltonian and the measurement observable. When the Hamiltonian and observable do not commute, the convergence is uniform towards the infinite-temperature state. Conversely, whenever the two operators have one or more eigenvectors in common in their spectral decomposition, the state of the monitored system converges differently in the subspaces spanned by the measurement observable eigenstates. As a result, we show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis, with a finite effective temperature in each measurement subspace. Finally, we quantify the effects of the quantum hardware noise on the data by modelling them by means of depolarizing quantum channels.
Abstract We study the dynamics of a three-dimensional generalization of Kitaev’s honeycomb lattice spin model (defined on the hyperhoneycomb lattice) subjected to a harmonic driving of J z , one of the three types of spin-couplings in the Hamiltonian. Using numerical solutions supported by analytical calculations based on a rotating wave approximation, we find that the system responds nonmonotonically to variations in the frequency ω (while keeping the driving amplitude J fixed) and undergoes dynamical freezing, where at specific values of ω, it gets almost completely locked in the initial state throughout the evolution. However, this freezing occurs only when a constant bias is present in the driving, i.e., when J z = J ′ + J cos ω t , with J ′ ≠ 0 . Consequently, the bias acts as a switch that triggers the freezing phenomenon. Dynamical freezing has been previously observed in other integrable systems, such as the one-dimensional transverse-field Ising model.
The validity of the ergodic hypothesis in quantum systems can be rephrased in the form of the eigenstate thermalization hypothesis (ETH), a set of statistical properties for the matrix elements of local observables in energy eigenstates, which is expected to hold in any ergodic system. We test the ETH in a nonintegrable model of relativistic quantum field theory (QFT) using the numerical method of Hamiltonian truncation in combination with analytical arguments based on Lorentz symmetry and renormalization group theory. We find that there is an infinite sequence of eigenstates with the characteristics of quantum many-body scars-that is, exceptional eigenstates with observable expectation values that lie far from thermal values-and we show that these states are one-quasiparticle states. We argue that in the thermodynamic limit the eigenstates cover the entire area between two diverging lines: the line of one-quasiparticle states, whose direction is dictated by relativistic kinematics, and the thermal average line. Our results suggest that the strong version of the ETH is violated in any relativistic QFT whose spectrum admits a quasiparticle description.