Witnessing environment dimension through temporal correlations
- URL: http://arxiv.org/abs/2305.19175v2
- Date: Fri, 5 Jan 2024 12:28:42 GMT
- Title: Witnessing environment dimension through temporal correlations
- Authors: Lucas B. Vieira, Simon Milz, Giuseppe Vitagliano, Costantino Budroni
- Abstract summary: We compute non-trivial bounds for sequences involving a qubit system and a qubit environment.
Our results provide a numerically tractable method to determine bounds on multi-time probability distributions in open quantum system dynamics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce a framework to compute upper bounds for temporal correlations
achievable in open quantum system dynamics, obtained by repeated measurements
on the system. As these correlations arise by virtue of the environment acting
as a memory resource, such bounds are witnesses for the minimal dimension of an
effective environment compatible with the observed statistics. These witnesses
are derived from a hierarchy of semidefinite programs with guaranteed
asymptotic convergence. We compute non-trivial bounds for various sequences
involving a qubit system and a qubit environment, and compare the results to
the best known quantum strategies producing the same outcome sequences. Our
results provide a numerically tractable method to determine bounds on
multi-time probability distributions in open quantum system dynamics and allow
for the witnessing of effective environment dimensions through probing of the
system alone.
Related papers
- Learning Controlled Stochastic Differential Equations [61.82896036131116]
This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion.
We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity.
Our method is available as an open-source Python library.
arXiv Detail & Related papers (2024-11-04T11:09:58Z) - Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.
We find sufficient conditions under which dynamical decoupling works for such systems.
Our bounds reproduce the correct scaling in various relevant system parameters.
arXiv Detail & Related papers (2024-09-24T04:58:28Z) - Geometry of sequential quantum correlations and robust randomness
certification [0.0]
We study the geometry of quantum correlations and their implications for robust device-independent randomness generation.
We identify a boundary for the set of these correlations expressed as a trade-off between the amount of nonlocality between different observers.
We propose a practical protocol based on non-projective measurements that can produce the boundary correlations under ideal conditions.
arXiv Detail & Related papers (2023-09-21T17:50:29Z) - Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning.
theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure.
This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
arXiv Detail & Related papers (2022-10-12T06:46:38Z) - Perturbation theory under the truncated Wigner approximation reveals how
system-environment entanglement formation drives quantum decoherence [0.0]
Quantum decoherence is the disappearance of simple phase relations within a discrete quantum system as a result of interactions with an environment.
We introduce a theoretical framework wherein we combine the truncated Wigner approximation with standard time-dependent perturbation theory.
We show that the selective suppression of low-frequency environmental modes is particularly effective for mitigating quantum decoherence.
arXiv Detail & Related papers (2022-06-22T18:17:28Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity.
For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles.
In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
arXiv Detail & Related papers (2021-12-22T15:27:30Z) - Sensing quantum chaos through the non-unitary geometric phase [62.997667081978825]
We propose a decoherent mechanism for sensing quantum chaos.
The chaotic nature of a many-body quantum system is sensed by studying the implications that the system produces in the long-time dynamics of a probe coupled to it.
arXiv Detail & Related papers (2021-04-13T17:24:08Z) - A discrete memory-kernel for multi-time correlations in non-Markovian
quantum processes [0.0]
We show that the transfer-tensor method can be extended to processes which include multiple interrogations.
Our approach exploits the process-tensor description of open quantum processes to represent and propagate the dynamics.
arXiv Detail & Related papers (2020-07-07T07:00:34Z) - Perturbation theory for operational quantum non-Markovianity [0.0]
We develop a perturbation theory that enables to express both joint probabilities and outcome correlations in terms of the unperturbed system density matrix propagator.
This object defines the open system dynamics in absence of measurement processes.
Using the perturbative approach, unusual memory effects induced by the interplay between the system-environment interaction and measurement processes are found in finite temperature reservoirs.
arXiv Detail & Related papers (2020-04-24T15:48:15Z)
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.