Invariant measures of randomized quantum trajectories

• URL: http://arxiv.org/abs/2603.28664v1
• Date: Mon, 30 Mar 2026 16:49:36 GMT
• Title: Invariant measures of randomized quantum trajectories
• Abstract summary: We explore the properties of quantum trajectories when the choice of probe observable is randomized.<n>We show that non-singular randomization ensures that quantum trajectories purify and therefore accept a unique invariant probability measure.<n>We introduce a new notion of ergodicity for quantum channels, which we call multiplicative primitivity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this article we explore the properties of quantum trajectories when the choice of probe observable is randomized. The randomization induces some regularization of the quantum trajectories. We show that non-singular randomization ensures that quantum trajectories purify and therefore accept a unique invariant probability measure. We furthermore study the regularity of that invariant measure. In that endeavour, we introduce a new notion of ergodicity for quantum channels, which we call multiplicative primitivity. It is a priory stronger than primitivity but weaker than positivity improving. Finally, we compute some invariant measures for canonical quantum channels and explore the limits of our assumptions with several examples.

Related papers

• Deterministic quantum trajectory via imaginary time evolution [4.06742798280037]
  Recent studies have highlighted that individual quantum trajectories encode essential physical information.<n>Direct observation of this effect is hindered by an exponential post-selection barrier.<n>We propose a deterministic method to efficiently prepare quantum trajectories in the probability of outcomes using imaginary time evolution.
  arXiv  Detail & Related papers  (2025-03-31T20:33:55Z)
• Quantum trajectory of the one atom maser [0.0]
  We consider a specific model of such a quantum trajectory associated to the one-atom maser model. When the system is non-resonant we prove that this Markov chain admits a unique invariant probability measure.
  arXiv  Detail & Related papers  (2024-03-29T10:11:37Z)
• Action formalism for geometric phases from self-closing quantum trajectories [55.2480439325792]
  We study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter.
  arXiv  Detail & Related papers  (2023-12-22T15:20:02Z)
• 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)
• Objectivity of classical quantum stochastic processes [0.0]
  We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable fulfill the Kolmogorov consistency condition. It can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.
  arXiv  Detail & Related papers  (2023-04-14T12:59:44Z)
• 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)
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain [62.997667081978825]
  We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization. In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
  arXiv  Detail & Related papers  (2022-12-19T12:34:37Z)
• Single-shot quantum measurements sketch quantum many-body states [7.89342891351528]
  We propose a nonlinear "measurement energy" based upon the measurement outcomes and an iterative effective-Hamiltonian approach to extract the most probable states. Our study paves the way towards concepts such as nonlinear-operator Hamiltonian and applications such as parent Hamiltonian reconstruction.
  arXiv  Detail & Related papers  (2022-03-02T19:00:24Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• 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)
• Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories [0.0]
  We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like variables. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system.
  arXiv  Detail & Related papers  (2020-03-18T18:32:47Z)

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.