An international research team proposes a measure that circumvents the problem of asymptotic quantification. The lead author of the paper, published in Nature Physics, is Ludovico Lami of the Scuola Normale Superiore in Pisa.
PISA, March 23, 2026. Quantum entanglement is the embodiment of the fact that quantum systems have a much richer structure than classical ones. Its key feature is that a quantum system can be more than just a sum of its parts, and the correlations between the parts of a large quantum system are what enables advantages of many quantum technologies. However, this richer structure is both a blessing and a curse. Understanding the properties of entanglement and optimal ways to use it requires us to characterise the behaviour of many systems together, and this typically leads to daunting formulas that require optimisation over many copies of quantum states and involve intractable asymptotic limits. This has fuelled the widespread view that exact and optimal ways to measure and detect entanglement are not possible to evaluate, hindering even a theoretical understanding of this key quantum resource.
A new international paper just published in Nature Physics (the first author of which is Ludovico Lami of the Scuola Normale, in collaboration with Mario Berta -RWTH Aachen, Germany- and Bartosz Regula -RIKEN Tokyo, Japan) challenges this common wisdom by showing that optimal, practically meaningful ways to measure entanglement are possible with just a single copy of a quantum state, without taking a many-copy limit. That is, merely a single copy can tell us how to optimally detect and extract entanglement, even if we could manipulate a vast number of such quantum systems together. This result is a unique phenomenon in the theory of quantum entanglement and shows that the understanding of ultimate, many-copy limits of the processing of quantum entanglement are not beyond our reach, after all.
To meaningfully quantify how much entanglement a quantum state possesses, it is natural to ask: How well can this entanglement be detected through measurements? How much of this entanglement can be extracted in a high-quality form that can be used in practice? These questions lead to the important operational tasks of entanglement testing and entanglement distillation (purification). “Our approach – says Lami - relies on a shift of perspective that adjusts the figures of merit of these fundamental tasks. We depart from the conventional focus on the quantity (yield) of distilled entanglement, but rather measure its quality (error). This simple conceptual shift leads to a precise equivalence between the two tasks and simplifying their structure”.
“Our key technical contribution – Lami continues - is then the resolution of a major problem in quantum state discrimination (hypothesis testing) related to distinguishing entangled states from unentangled ones. We extend state-of-the-art mathematical techniques in quantum state discrimination to tackle this problem. We show that this optimal solution is given by a measure of entanglement known as the 'reverse relative entropy of entanglement', giving it a twofold interpretation as the optimal figure of merit of both entanglement testing and distillation, and establishing it as a meaningful measure of entanglement that can be computed with just a single copy of a quantum state”.
“The importance of quantum entanglement in quantum communication and computation means that our results will find direct use in the study of this powerful yet perplexing phenomenon. The realisation that even the ultimate limits of entanglement detection and extraction can be quantified opens the door to an efficient understanding of this important resource. Furthermore, our technical developments are major advances in quantum state discrimination, showing that even much more complicated problems than those solved before can admit exact, computable solutions”.
