An introduction to monitored quantum systems and quantum trajectories: spectrum, typicality, and phases
- URL: http://arxiv.org/abs/2512.19922v1
- Date: Mon, 22 Dec 2025 22:59:16 GMT
- Title: An introduction to monitored quantum systems and quantum trajectories: spectrum, typicality, and phases
- Authors: Ryusuke Hamazaki, Ken Mochizuki, Hisanori Oshima, Yohei Fuji,
- Abstract summary: We provide an introductory theoretical review on the basic formalisms governing open quantum dynamics under measurement.<n>We introduce the concept of quantum trajectories, which are the conditional dynamics of monitored states shaped by a set of measurement outcomes.<n>Lyapunov exponents of typical quantum trajectories serve as indicators of measurement-induced phase transitions in monitored quantum many-body systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Thanks to recent experimental advances in simulating and detecting quantum dynamics with high precision and controllability, our understanding of the physics of monitored quantum systems has considerably deepened over the past decades. In this article, we provide an introductory theoretical review on the basic formalisms governing open quantum dynamics under measurement, along with recent developments in their spectral and typical aspects. After reviewing quantum measurement theory, we introduce the concept of quantum trajectories, which are the conditional dynamics of monitored states shaped by a set of measurement outcomes. We then discuss the spectral properties of the dynamical map describing the evolution averaged over measurement outcomes. As has recently been recognized, these spectral features are intimately connected to whether quantum trajectories exhibit typical behaviors, such as the ergodicity and purification. Moreover, we introduce Lyapunov exponents of typical quantum trajectories and discuss how these quantities serve as indicators of measurement-induced phase transitions in monitored quantum many-body systems.
Related papers
- Tailoring Quantum Chaos With Continuous Quantum Measurements [0.0]
We show that quantum monitoring can tailor the signatures of quantum chaos in the dynamics.<n>A typical quantum trajectory obtained by monitoring with unit efficiency exhibits enhanced quantum chaos relative to the average dynamics.
arXiv Detail & Related papers (2026-02-02T19:00:03Z) - Post-processed estimation of quantum state trajectories [0.0]
We show that future information can be incorporated when reconstructing the trajectories of quantum states.<n>These results establish that future information can enhance quantum trajectory reconstruction, with potential applications across quantum sensing, control, and error correction.
arXiv Detail & Related papers (2025-10-19T08:37:09Z) - Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
We explore the applicability of quantum-data learning to practical problems in high-energy physics.
We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states.
The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
arXiv Detail & Related papers (2023-06-29T18:00:01Z) - Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories.
The measurements are applied to the entire system, having the effect of projecting the system into a product state.
arXiv Detail & Related papers (2023-05-06T18:09:17Z) - Quantifying measurement-induced quantum-to-classical crossover using an
open-system entanglement measure [49.1574468325115]
We study the entanglement of a single particle under continuous measurements.
We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
arXiv Detail & Related papers (2023-04-06T09:45:11Z) - Monitored Quantum Dynamics and the Kitaev Spin Liquid [0.0]
Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter.
Motivated by the physics of the Kitaev quantum spin liquid, we study quantum circuit dynamics in (2+1)-dimensions involving local projective measurements.
arXiv Detail & Related papers (2022-07-06T18:00:07Z) - Experimental Realization of a Measurement-Induced Entanglement Phase
Transition on a Superconducting Quantum Processor [0.0]
We report the realization of a measurement-induced entanglement transition on superconducting quantum processors with mid-circuit readout capability.
Our work paves the way for the use of mid-circuit measurement as an effective resource for quantum simulation on near-term quantum computers.
arXiv Detail & Related papers (2022-03-08T19:01:04Z) - Observing a Topological Transition in Weak-Measurement-Induced Geometric
Phases [55.41644538483948]
Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control.
We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength.
Our results open new horizons for measurement-enabled quantum control of many-body topological states.
arXiv Detail & Related papers (2021-02-10T19:00:00Z) - Unraveling the topology of dissipative quantum systems [58.720142291102135]
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories.
We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
arXiv Detail & Related papers (2020-07-12T11:26:02Z) - Quantum Zeno effect appears in stages [64.41511459132334]
In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates.
We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
arXiv Detail & Related papers (2020-03-23T18:17:36Z) - Detecting dynamical quantum phase transition via out-of-time-order
correlations in a solid-state quantum simulator [12.059058714600607]
We develop and experimentally demonstrate that out-of-time-order correlators can be used to detect nonoequilibrium phase transitions in the transverse field Ising model.
Further applications of this protocol could enable studies other of exotic phenomena such as many body localization, and tests of the holographic duality between quantum and gravitational systems.
arXiv Detail & Related papers (2020-01-17T14:28:42Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.