Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillae are not reinitialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillae and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.
Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillae are not reinitialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillae and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.
We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (``detectors''), which are periodically measured by means of strong projective measurements. The concentration ${\ensuremath{\rho}}_{a}$ of ancillae and their coupling M to the main system are considered as parameters. We explore the dynamics of density and of entanglement entropy in the chain, for various values of ${\ensuremath{\rho}}_{a}$ and M for two models of the detector-chain interaction that couple the local density in the chain to a detector degree of freedom. It is found that, for the density-density (Szsz-type in spin language) coupling, the critical values Mc for the measurement-induced entanglement transition depends sensitively on ${\ensuremath{\rho}}_{a}$. Moreover, our results indicate that for a sufficiently small ${\ensuremath{\rho}}_{a}$ the transition in this model disappears; i.e., a finite density of detectors is needed to reach a disentangling phase. The behavior is qualitatively different for the second model, with density-hopping (Szsx-type) coupling. Specifically, the dynamics is much less sensitive to the concentration ${\ensuremath{\rho}}_{a}$ of detectors than in the first model. Furthermore, the dependence of entanglement on the coupling strength M is strongly nonmonotonic, indicating reentrance of the entangling phase at large M.
We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.
In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin 1/2 system with next-nearest-neighbour exchange interactions(K), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction Kc and in the valance bond solid phase above Kc. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory (↓↓) describing a uniform measurement outcome given the all ancilla spins initiated in the same (↓) state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when K<Kc whereas it weakly decreases when K>Kc. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.
We introduce and explore a one-dimensional ``hybrid'' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a ``quantum Zeno phase'' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable ``weak measurement phase'' that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the ``weak measurement phase'' and the ``quantum Zeno phase,'' driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this quantum entanglement transition are accessed.
We address here the issue of quantum measurement in which the interaction between the system at hand and the measuring apparatus causes a collapse of the wave function or the density operator. The analysis is carried out for the prototypical tight-binding chain involving a quantum particle hopping between nearest-neighbour sites on a lattice, with the system subject to repeated projective measurements to a detector site. However, unlike previous work, the measurements are performed at random times. In the absence of measurement, the particle while starting from a site is known to spread out to farther sites as time progresses, leading to complete delocalization of the particle in time. In presence of measurements, we derive exact results for the probability at a given time for the particle to be found on different sites and averaged with respect to different realizations of the dynamics. We consider the representative case in which the time gap between successive measurements are sampled independently from an exponential distribution. The novel result of our findings is the revelation of the striking effect of Stochastic Localization, whereby the particle has at long times time-independent probabilities to be on different sites. This implies localization of the particle at long times, achieved through classical stochasticity involved with the random times for measurements. An extreme case of such localization is attained if the measurements are done very frequently, when the particle is completely localized at the detector site! We also point out the stochastic version of the Zeno effect, whereby dynamical evolution of a quantum system is arrested through repeated measurements at frequent-enough times. In the wake of recent experiments on projective measurements at random times achieved through randomly-pulsed sequences, our proposition is amenable to experimental realization.