Quantifying unknown quantum states: Study explores effectiveness of existing methods

December 8, 2025 feature Quantifying unknown quantum states: Study explores effectiveness of existing methods by Ingrid Fadelli, Phys.org edited by Lisa Lock, reviewed by Robert Egan Editors' notes This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: fact-checked peer-reviewed publication trusted source proofread The GIST Add as preferred source Pictorial representation of a quantum-state tomography algorithm. Credit: Nature Physics (2025). DOI: 10.1038/s41567-025-03086-2 Reliably quantifying and characterizing the quantum states of various systems is highly advantageous for both quantum physics research and the development of quantum technologies. Quantifying these states typically entails performing several measurements and reconstructing them via a process known as quantum-state tomography. Researchers at Freie Universität Berlin, Scuola Normale Superiore in Italy and other institutes recently carried out a study aimed at shedding light on the accuracy with which tomography can reliably reconstruct different quantum states in systems that vary in size. Their findings, published in Nature Physics, suggest that the tomography of these states is highly inefficient in systems described by continuous degrees of freedom, such as modes of light in bosonic and quantum-optical systems. "Notions of quantum state tomography have a long tradition," Jens Eisert, co-author of the paper, told Phys.org. "After all, in any experiment, data is ultimately all we ever have, so it is natural to think about how to learn unknown quantum states from the data we collect. Such ideas have been particularly prominent in quantum optical systems, where state preparation has an especially long history." Probing the limits of quantum state tomography The term "tomography" first originated within the field of medical imaging. In this context, this is a process via which medical experts reconstruct higher-dimensional objects from lower-dimensional projections. Notably, this reconstruction is also applicable in the context of quantum optics. "Methods of quantum state tomography date back to the 1980s and earlier," said Eisert. "More recently, researchers have begun to think about state preparation and characterization in more precise, quantitative terms. Motivated by rapid progress in quantum technologies, people now ask what can be achieved reliably with realistic experimental resources. This is also the perspective we adopted." Drawing from the recent advancement of quantum technologies, Eisert and his colleagues set out to delineate the accuracy with which one can learn unknown quantum states from data. They looked at two distinct types of states, Gaussian (i.e., fully described by their first and second statistical moments) and non-Gaussian (i.e., exhibiting features beyond so-called Gaussian statistics) states. "We were genuinely surprised when we realized just how difficult this problem is: the sample complexity grows extremely unfavorably with the desired accuracy of the reconstruction," explained Eisert. "Quantum state tomography for continuous-variable systems is typically performed using homodyne or heterodyne detection—techniques that naturally align with the continuous nature of light. These methods also provide valuable insights into the structure of the quantum state under investigation." The strengths and limits of existing tomography techniques The results of this study highlight the limitations of existing approaches for characterizing quantum states. Specifically, they show that quantum-state tomography is significantly more challenging for continuous-variable systems than for finite-dimensional systems. "The core surprise for us was that the established approaches are strongly challenged by complexity-theoretic bounds," said Eisert. "It is, after all, extremely difficult to accurately learn unknown continuous-variable quantum states, regardless of the specific method employed. This remains true even under natural constraints on energy and moments." The recent work by Eisert and his colleagues sheds new light on what can be realistically measured in quantum systems using current approaches and what cannot. The insight gathered by the team could guide future efforts aimed at characterizing quantum states in emerging quantum and quantum-optical devices. "Maybe the most notable contribution of our paper, at least from a cultural standpoint, is that it demonstrates the advantages of prompting communication between researchers from different subfields," said Eisert. "One should not take old results for granted. It is worthwhile to revisit old questions to find out how well an approach can really work. Physically speaking, the infinite-dimensional nature of states of light makes it very difficult to determine what is going on in a laboratory." The researchers plan to continue assessing the effectiveness and scalability of existing methods for quantifying quantum states. This will in turn help them to develop increasingly advanced and better performing quantum technologies. "We are now eager to establish an operational theory of learning in the quantum world," added Eisert. "More broadly, we aim to understand what one can truly infer about physical systems in nature from a reasonable, and ideally polynomial, amount of data." Written for you by our author Ingrid Fadelli, edited by Lisa Lock, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. More information: Francesco A. Mele et al, Learning quantum states of continuous-variable systems, Nature Physics (2025). DOI: 10.1038/s41567-025-03086-2 Journal information: Nature Physics © 2025 Science X Network Citation: Quantifying unknown quantum states: Study explores effectiveness of existing methods (2025, December 8) retrieved 7 January 2026 from https://phys.org/news/2025-12-quantifying-unknown-quantum-states-explores.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. 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