Temporal State Tomography via Quantum Snapshotting the Temporal Quasiprobabilities

TL;DR

This paper introduces temporal state tomography (TST), a new method for reconstructing multi-time quantum processes using temporal quasiprobability distributions, unifying state and channel reconstruction.

Contribution

The authors develop a unified framework for temporal state tomography based on TQDs, including operational measurement procedures and sample complexity analysis.

Findings

TST provides a complete description of multi-time quantum processes.

Any TQD can be obtained through classical post-processing of measurement data.

The sample complexity of TST quantifies its statistical efficiency.

Abstract

Quantum tomography is a cornerstone of quantum information science, enabling the reconstruction of states and channels from experimental data. Here we introduce a new paradigm, temporal state tomography (TST), for reconstructing quantum processes across multiple times. Our approach is based on temporal quasiprobability distributions (TQDs), which, in the informationally complete setting, provide a complete description of multi-time quantum processes and uniquely determine temporal states. We formulate TST as a unified framework for reconstructing both density operators and quantum channels within a single scheme. We show that any TQD can be obtained via classical post-processing of measurement outcomes generated by a fixed set of quantum instruments, thereby establishing a direct operational route to accessing TQDs experimentally. For informationally complete TQDs, the associated temporal state can be reconstructed via a temporal Bloch-type representation. Leveraging this correspondence, we derive the sample complexity of TST, thereby quantifying its statistical efficiency.