Quantum memory surpasses classical limits for storing unknown quantum operations

June 9, 2026 feature Quantum memory surpasses classical limits for storing unknown quantum operations Ingrid Fadelli Author Sadie Harley Scientific Editor Robert Egan Associate Editor Quantum memories, systems that store and retrieve information leveraging quantum mechanical effects, can outperform classical storage systems on some existing tasks. Yet these promising memories could also complete operations that are very difficult or impossible for classical systems, including the storage and retrieval of so-called isometry channels. Isometry channels are transformations that entail mapping a smaller quantum system onto a larger one while preserving quantum information. In a paper published in Physical Review Letters, researchers at the University of Tokyo showed that quantum methods significantly outperform classical ones in the storage and retrieval of these transformations. "This work was motivated by a very simple question: When is it truly useful to store quantum information in quantum memory, rather than first extracting classical information from it?" Satoshi Yoshida, first author of the paper, told Phys.org. "In quantum information processing, we often consider unknown quantum operations, or 'black box' operations, and ask whether they can be stored and later retrieved. For unitary operations, it was known that a classical strategy is already optimal. On the other hand, we generally expect quantum memory to be more powerful than classical memory." Assessing quantum memories in isometry channel operations Yoshida and his colleagues wanted to assess the performance of quantum memories in a nonclassical task, specifically the storage and subsequent retrieval of unknown isometry channels. This task can be compared to storing a program so that it can be used later, yet in this case the program is an unidentified quantum operation. "We wanted to test whether a genuine advantage of quantum memory can appear for a broader and very important class of quantum operations called isometry channels," explained Yoshida. "The primary objective of our paper was to provide a rigorous comparison between two approaches: a classical strategy, where one first estimates the unknown operation, and a quantum strategy, where one stores it directly as a quantum state without identifying it." As part of their study, Yoshida and his colleagues compared a classical and a quantum strategy for retrieving unknown isometry channels. The classical strategy achieves this by repeatedly probing the channel—i.e., quantum operation—to estimate what it is, then storing this estimate as classical data that can be used to reconstruct the operation later. The quantum strategy, on the other hand, stores the effect of the unknown operation directly, in the form of a quantum state known as a "program state." This is done without fully uncovering what the stored operation is. "To demonstrate a quantum advantage, we first derived the best possible performance of any classical strategy based on estimating the isometry channel," said Yoshida. "This was the technically important part, because to prove a quantum advantage, one must compare it against the best possible classical method, not just a particular classical method. We showed that the classical estimation strategy is limited by the standard quantum limit." The researchers later compared the performance of the optimal classical benchmark they identified with that of a quantum strategy rooted in an approach known as port-based teleportation. This quantum strategy stores an unknown channel operation in a quantum program state that can be efficiently retrieved at a later stage. "In terms of the number of times the unknown operation must be used, the quantum strategy achieves a quadratic improvement over the best classical strategy," said Yoshida. "This provides a rigorous example in which quantum memory outperforms classical memory for storing and retrieving an unknown quantum operation." Implications for the advancement of quantum memories The results of this study highlight the potential of quantum approaches for the storage and retrieval of unknown quantum operations, showing that these approaches outperform the best existing classical strategy. Notably, the quantum strategy used by the researchers could also be applied to the storage and retrieval of other types of quantum operations. "I think the most notable contribution of our study is that we identified the fundamental limitation of classical strategies for isometry channels," said Yoshida. "By deriving the optimal estimation performance, we could show that the gap between classical and quantum strategies is not an artifact of comparing against a weak classical method, but a genuine separation." The researchers' recent work also shed new light on the strengths of quantum memories and how they could serve as a resource to further advance quantum technologies. As the quantum strategy they used can store operations without fully uncovering them, it might eventually also allow devices to run quantum operations while keeping some information hidden or private. "One direction for further research will be to consider the program cost, which is the number of qubits required to store unknown quantum operations," said Yoshida. "For the unitary channel, the minimum program cost is also achieved by the classical strategy and is related to the number of parameters needed to describe the unitary operator. However, for isometry channels, the minimum program cost remains open. We have shown that the program cost can be made smaller than the number of parameters needed to describe the isometry operator, but we still do not know its minimum value." As part of their next studies, Yoshida and his colleagues would also like to explore the possibility of retrieving multiple copies of the stored operation using their proposed quantum strategy and a classical benchmark. In this scenario, they think that the disparity between quantum and classical memories might shift considerably. "In a classical strategy, once we have estimated the unknown operation, the estimator can be copied and reused to generate multiple copies of the output," added Yoshida. "A quantum strategy can also be extended to this setting, for example, by using multi-port-based teleportation, which allows several quantum states to be teleported simultaneously. Intuitively, one might expect the classical strategy to become more competitive when multiple copies are required, because classical information can be copied freely. However, its performance is still limited by genuinely quantum constraints, such as the no-cloning theorem for unitary channels. "Comparing the optimal classical and quantum strategies for the storage and retrieval of multiple copies of an input operation is thus a natural and important open problem." Written for you by our author Ingrid Fadelli, edited by Sadie Harley, 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. Publication details Satoshi Yoshida et al, Quantum Advantage in Storage and Retrieval of Isometry Channels, Physical Review Letters (2026). DOI: 10.1103/fdvq-9m8m. On arXiv: DOI: 10.48550/arxiv.2507.10784 Journal information: Physical Review Letters , arXiv Key concepts Information & communication theoryQuantum algorithms & computationQuantum correlations, foundations & formalism© 2026 Science X Network