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  • Open Access

Tensor Network Approach to Sensing Quantum Light-Matter Interactions

Aiman Khan1,*,†, Francesco Albarelli2,*,‡, and Animesh Datta3,§

  • *A.K. and F.A. contributed equally to this work.
  • †Contact author: aimankhan1509@protonmail.com
  • ‡Contact author: francesco.albarelli@gmail.com
  • §Contact author: animesh.datta@warwick.ac.uk
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PRX Quantum 6, 040343 – Published 21 November, 2025

DOI: https://doi.org/10.1103/ljh3-3l4j

Abstract

We present the fundamental limits to the precision of estimating parameters of a quantum matter system probed by light, even when some of the light is lost. This practically inevitable scenario leads to a tripartite quantum system of matter, and light—detected and lost. Evaluating fundamental information theoretic quantities such as the quantum Fisher information of only the detected light was heretofore impossible. We succeed by expressing the final quantum state of the detected light as a matrix product operator. We apply our method to resonance fluorescence and pulsed spectroscopy. For both, we quantify the sub-optimality of continuous homodyning and photo-counting measurements in parameter estimation. For the latter, we find that single-photon Fock state pulses allow higher precision per photon than pulses of coherent states. Our method should be valuable in studies of quantum light-matter interactions, quantum light spectroscopy, quantum stochastic thermodynamics, and quantum clocks.

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Popular Summary

Spectroscopy is the science, and art, of learning about inaccessibly small systems such as atoms and molecules by shining light on them and measuring what is scattered. Spectroscopy has advanced spectacularly over the past century, becoming increasingly more precise. Some natural questions arise: What is the fundamental limit to how precise spectroscopy can be? How can that be calculated theoretically and attained experimentally?

We answer these questions for a two-level system probed by classical (laser) light. A crucial aspect is to deal with losses, as all the scattered light can never be detected. The fundamental precision of spectroscopy is determined by the quantum Fisher information (QFI), a highly nonlinear function of the quantum state of the detected light.

The QFI for the lossless case was first evaluated in 2014. Since then, evaluating the QFI of the detected light in the lossy case, which results in a mixed quantum state, had been open. We succeed by combining two previously known but unrelated ideas: an efficient description of the quantum state of the detected light as a matrix product operator (MPO) and a variational algorithm for evaluating the QFI of an MPO.

Our work should provide the fundamental precision of several spectroscopic techniques to compare them with existing experiments using laser light, as well as future ones using quantum states of light. It also shows how classical light develops nonclassical correlations after interacting with quantum matter. This should be of interest in wider atomic, molecular, and optical physics and quantum technologies.

Article Text

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PRX Quantum 6, 040343– Published 21 November, 2025
  • Received 24 April 2025
  • Revised 8 July 2025
  • Accepted 13 August 2025
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