Detecting Initial System-Environment Correlations from a Single Observable

• URL: http://arxiv.org/abs/2602.18516v1
• Date: Thu, 19 Feb 2026 19:37:36 GMT
• Title: Detecting Initial System-Environment Correlations from a Single Observable
• Authors: Ali Abu-Nada, Russell Ceballos, Lian-Ao Wu,
• Abstract summary: We show that for a known interaction, it can be sufficient to monitor a single expectation value of the system.<n>We show that the same single-observable logic extends to an exactly solvable pure-dephasing spin--boson model with an infinite environment.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of detecting initial system--environment correlations when the environment is not directly accessible. Most existing approaches rely on full state tomography or multiple system preparations, which can be experimentally demanding. We show that, for a known interaction, it can be sufficient to monitor a single expectation value of the system. Focusing on a qubit interacting with an environment via isotropic Heisenberg exchange, we derive exact bounds on the signal $z(t)=\langleσ_z^S\rangle(t)$ that hold for all factorized initial states. These bounds define a \emph{factorized envelope}: if an observed trajectory exits this envelope at any time, initial system--environment correlations are certified. From a reduced-dynamics perspective, the envelope admits a clear operational interpretation as the admissible region generated by the standard product assignment (embedding) map, which serves as a null model for uncorrelated preparations. Envelope violations therefore rule out the entire product-assignment class using only a single calibrated observable. We illustrate the method using three families of correlated initial states and observe clear envelope violations, including cases in which the reduced system state is maximally mixed. We further show that the same single-observable logic extends to an exactly solvable pure-dephasing spin--boson model with an infinite environment, where factorized initial states generate a simple coherence envelope whose violation certifies initial correlations. Overall, our results demonstrate that single-axis measurements, combined with a one-time calibration of $ρ_S(0)$, can certify initial system--environment correlations without tomography or environment access.

Related papers

• Combating Noisy Labels through Fostering Self- and Neighbor-Consistency [120.4394402099635]
  Label noise is pervasive in various real-world scenarios, posing challenges in supervised deep learning.<n>We propose a noise-robust method named Jo-SNC (textbfJoint sample selection and model regularization based on textbfSelf- and textbfNeighbor-textbfConsistency)<n>We design a self-adaptive, data-driven thresholding scheme to adjust per-class selection thresholds.
  arXiv  Detail & Related papers  (2026-01-19T07:55:29Z)
• Phase-space entropy at acquisition reflects downstream learnability [54.4100065023873]
  We propose an acquisition-level scalar $S_mathcal B$ based on instrument-resolved phase space.<n>We show theoretically that (S_mathcal B) correctly identifies the phase-space coherence of periodic sampling.<n>$|S_mathcal B|$ consistently ranks sampling geometries and predicts downstream reconstruction/recognition difficulty emphwithout training.
  arXiv  Detail & Related papers  (2025-12-22T10:03:51Z)
• Identifying General Mechanism Shifts in Linear Causal Representations [58.6238439611389]
  We consider the linear causal representation learning setting where we observe a linear mixing of $d$ unknown latent factors. Recent work has shown that it is possible to recover the latent factors as well as the underlying structural causal model over them. We provide a surprising identifiability result that it is indeed possible, under some very mild standard assumptions, to identify the set of shifted nodes.
  arXiv  Detail & Related papers  (2024-10-31T15:56:50Z)
• Learning a Fast Mixing Exogenous Block MDP using a Single Trajectory [87.62730694973696]
  STEEL is the first provably sample-efficient algorithm for learning the controllable dynamics of an Exogenous Block Markov Decision Process from a single trajectory.<n>We prove that STEEL is correct and sample-efficient, and demonstrate STEEL on two toy problems.
  arXiv  Detail & Related papers  (2024-10-03T21:57:21Z)
• Probability vector representation of the Schrödinger equation and Leggett-Garg-type experiments [0.0]
  Leggett-Garg inequalities place bounds on the temporal correlations of a system based on the principles of macroscopic realism. We propose a scheme to describe the dynamics of generic $N$-level quantum systems via a probability vector representation of the Schr"odinger equation. We also define a precise notion of no-signaling in time (NSIT) for the probability distributions of noncommuting observables.
  arXiv  Detail & Related papers  (2023-12-26T19:00:00Z)
• Initial correlations in open quantum systems are always detectable [0.0]
  We show that initial correlations between the system and the environment are always detectable. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable.
  arXiv  Detail & Related papers  (2023-11-07T10:04:40Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• 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)
• E-detectors: a nonparametric framework for sequential change detection [86.15115654324488]
  We develop a fundamentally new and general framework for sequential change detection. Our procedures come with clean, nonasymptotic bounds on the average run length. We show how to design their mixtures in order to achieve both statistical and computational efficiency.
  arXiv  Detail & Related papers  (2022-03-07T17:25:02Z)
• Adapted projection operator technique for the treatment of initial correlations [0.0]
  We introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Our method is further illustrated by means of two cases study, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.
  arXiv  Detail & Related papers  (2021-07-28T18:01:12Z)
• Detecting Initial System-Environment Correlations in Open Systems [0.0]
  Correlations between a system and its environment lead to errors in an open quantum system. We show that we can detect correlations by only measuring the system itself.
  arXiv  Detail & Related papers  (2021-04-04T21:13:35Z)
• Initial entanglement, entangling unitaries, and completely positive maps [0.0]
  We study the interplay between the initial correlations and the unitary applied. For almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. We obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.
  arXiv  Detail & Related papers  (2020-12-22T19:04:42Z)

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.