Detecting Initial System-Environment Correlations from a Single Observable
Sharjah Maritime Academy（沙迦海事学院）；Department of Physical Sciences, Olive-Harvey College, City Colleges of Chicago（芝加哥城市学院奥莉-哈维学院物理科学系）；QuSTEAM Initiative（QuSTEAM倡议）；Department of Physics, University of the Basque Country UPV/EHU（巴斯克大学UPV/EHU物理系）；EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学UPV/EHU量子中心）
Ali Abu-Nada, Russell Ceballos, Lian-Ao Wu
备注：
The manuscript is 12 pages long and includes 5 figures. Comments are welcome
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.
Detecting nonequilibrium phase transitions via continuous monitoring of space-time trajectories and autoencoder-based clustering
Institut für Theoretische Physik, Universität Tübingen（蒂宾根大学理论物理研究所）；Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques（巴黎西岱大学、法国国家科学研究中心、物质与量子现象）；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；The University of Nottingham（诺丁汉大学）
