Snapshotting Quantum Dynamics at Multiple Time Points

TL;DR

This paper introduces a method to reconstruct quantum dynamics at multiple time points using ancilla-assisted measurements and classical post-processing, enabling the extraction of correlation functions and quantum coherence effects.

Contribution

The authors propose a novel snapshotting protocol for quantum systems that cancels measurement disturbance effects, allowing multi-time quantum statistics reconstruction.

Findings

Successfully demonstrated multi-time QPD reconstruction in a trapped-ion system.

Revealed quantum coherence contributions through negativity in the QPDs.

Extracted multiple correlation functions with various time orderings experimentally.

Abstract

Measurement-induced state disturbance is a major challenge in obtaining quantum statistics at multiple time points. We propose a method to extract dynamic information from a quantum system at intermediate time points, namely snapshotting quantum dynamics. To this end, we apply classical post-processing after performing the ancilla-assisted measurements to cancel out the impact of the measurements at each time point. Based on this, we reconstruct a multi-time quasi-probability distribution (QPD) that correctly recovers the probability distributions at the respective time points. Our approach can also be applied to simultaneously extract exponentially many correlation functions with various time-orderings. We provide a proof-of-principle experimental demonstration of the proposed protocol using a dual-species trapped-ion system by employing $^{171}\rm{Yb}^+$ and $^{138}\rm{Ba}^+$ ions as the system and the ancilla, respectively. Multi-time measurements are performed by repeated initialization and detection of the ancilla state without directly measuring the system state. The two- and three-time QPDs and correlation functions are reconstructed reliably from the experiment, negativity and complex values in the QPDs clearly indicate a contribution of the quantum coherence throughout dynamics.