Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements

• URL: http://arxiv.org/abs/2404.03168v2
• Date: Tue, 4 Jun 2024 21:36:27 GMT
• Title: Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements
• Authors: Owen Ekblad, Eloy Moreno-Nadales, Lubashan Pathirana, Jeffrey Schenker,
• Abstract summary: We study quantum trajectories resulting from repeated random measurements subject to stationary noise. The resulting trajectory of quantum states is a time-inhomogeneous Markov chain in a random environment. We prove that purification occurs if and only if this collection of random subspaces is empty.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a general framework to study quantum trajectories resulting from repeated random measurements subject to stationary noise, and generalize results of K\"ummerer and Maassen to this setting. The resulting trajectory of quantum states is a time-inhomogeneous Markov chain in a random environment. K\"ummerer and Maassen introduced the concept of dark subspaces for noise-free processes, establishing that their absence is equivalent to asymptotic purification of the system state. We clarify the notion of dark subspaces in the disordered setting by defining a measurable correspondence consisting of a collection of random subspaces satisfying a darkness condition. We further prove that asymptotic purification occurs if and only if this collection of random dark subspaces is empty. Several examples of these phenomena are provided.

Related papers

• Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization [6.405171754125318]
  We develop a theory of random non-Hermitian action that describes the nonlinear dynamics of quantum states in Hilbert space. We investigate the evolution of a single-particle Gaussian wave packet under the influence of non-Hermiticity and randomness.
  arXiv  Detail & Related papers  (2024-10-14T05:15:18Z)
• Repeated measurements and random scattering in quantum walks [0.0]
  We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. We conclude that repeated measurements as well as random scattering provide efficient tools for controlling quantum walks.
  arXiv  Detail & Related papers  (2024-05-30T15:27:55Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• A note on typicality in random quantum scattering [0.0]
  We consider scattering processes where a quantum system is comprised of an inner subsystem and of a boundary. We show that, regardless of the initial state, a single scattering event will disentangle the unconditional state across the inner subsystem-boundary partition.
  arXiv  Detail & Related papers  (2023-08-29T17:42:25Z)
• 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)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Discord and Decoherence [0.0]
  We investigate how quantum discord is modified by a quantum-to-classical transition. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity.
  arXiv  Detail & Related papers  (2021-12-09T17:01:54Z)
• 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 Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit [0.0]
  The time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol. For a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-02T13:29:22Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.