- Editors' Suggestion
- Open Access
How to use arbitrary measuring devices to perform almost-perfect measurements
Phys. Rev. A 112, 022405 – Published 1 August, 2025
DOI: https://doi.org/10.1103/8tph-mc2p
Abstract
We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available “imperfect” devices a small number of times to implement a target measurement with average error that drops off exponentially with the number of imperfect measurements used. We hope that could be useful in near-term applications as a type of lightweight error mitigation of the measuring devices. As well as the view to practical applications, we consider the question from a general theoretical perspective in the most general setting where both the available and target measurements are arbitrary generalized quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of (complete) von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon “classical cloning” can perfectly achieve this task. We show that asymptotically any nontrivial quantum measurement can reproduce any other. We also study optimal protocols for a fixed number of uses of the available measurement. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Furthermore, we show that, in a setting where we perform multiple measurements in parallel, we can achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory. Finally, we show that advantages can also be gained by making use of probabilistic protocols.
Physics Subject Headings (PhySH)
Article Text
References (20)
- H. P. Yuen, Design of transparent optical networks by using novel quantum amplifiers and sources, Opt. Lett. 12, 789 (1987).
- M. Dall'Arno, G. M. D'Ariano, and M. F. Sacchi, Purification of noisy quantum measurements, Phys. Rev. A 82, 042315 (2010).
- R. Hicks, B. Kobrin, C. W. Bauer, and B. Nachman, Active readout-error mitigation, Phys. Rev. A 105, 012419 (2022).
- J. M. Günther, F. Tacchino, J. R. Wootton, I. Tavernelli, and P. K. Barkoutsos, Improving readout in quantum simulations with repetition codes, Quantum Sci. Technol. 7, 015009 (2022).
- A. Abbas, S. Andersson, A. Asfaw, A. Corcoles, L. Bello, Y. Ben-Haim, M. Bozzo-Rey, S. Bravyi, N. Bronn, L. Capelluto, A. C. Vazquez, J. Ceroni, R. Chen, A. Frisch, J. Gambetta, S. Garion, L. Gil, S. D. L. P. Gonzalez, F. Harkins, T. Imamichi et al., Learn quantum computation using qiskit (2020), https://github.com/Qiskit/textbook.
- Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T. E. O'Brien, Quantum error mitigation, Rev. Mod. Phys. 95, 045005 (2023).
- D. B. Hume, T. Rosenband, and D. J. Wineland, High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements, Phys. Rev. Lett. 99, 120502 (2007).
- M. Sinhal, Z. Meir, K. Najafian, G. Hegi, and S. Willitsch, Quantum-nondemolition state detection and spectroscopy of single trapped molecules, Science 367, 1213 (2020).
- M. Raha, S. Chen, C. M. Phenicie, S. Ourari, A. M. Dibos, and J. D. Thompson, Optical quantum nondemolition measurement of a single rare earth ion qubit, Nat. Commun. 11, 1605 (2020).
- S. Motlakunta, N. Kotibhaskar, C.-Y. Shih, A. Vogliano, D. McLaren, L. Hahn, J. Zhu, R. Hablützel, and R. Islam, Preserving a qubit during state-destroying operations on an adjacent qubit at a few micrometers distance, Nat. Commun. 15, 6575 (2024).
- E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
- P. Skrzypczyk and N. Linden, Robustness of measurement, discrimination games, and accessible information, Phys. Rev. Lett. 122, 140403 (2019).
- M. Oszmaniec and T. Biswas, Operational relevance of resource theories of quantum measurements, Quantum 3, 133 (2019).
- R. Takagi and B. Regula, General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks, Phys. Rev. X 9, 031053 (2019).
- T. Guff, N. A. McMahon, Y. R. Sanders, and A. Gilchrist, A Resource theory of quantum measurements, J. Phys. A: Math. Theor. 54, 225301 (2021).
- C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993).
- L. Guerini, J. Bavaresco, M. Terra Cunha, and A. Acín, Operational framework for quantum measurement simulability, J. Math. Phys. 58, 092102 (2017).
- M. Oszmaniec, L. Guerini, P. Wittek, and A. Acín, Simulating positive-operator-valued measures with projective measurements, Phys. Rev. Lett. 119, 190501 (2017).
- C. Leang and D. Johnson, On the asymptotics of M-hypothesis Bayesian detection, IEEE Trans. Inf. Theory 43, 280 (1997).
- F. B. Maciejewski, Z. Puchała, and M. Oszmaniec, Exploring quantum average-case distances: Proofs, properties, and examples, IEEE Trans. Inf. Theory 69, 4600 (2023); Operational quantum average-case distances, Quantum 7, 1106 (2023).
