Search

Acknowledgements: We acknowledge the use of IBM Quantum services and the Rigetti Aspen-9 processor for this work. The views expressed are those of the authors, and do not reflect the official policy or position of IBM, the IBM Quantum team or Rigetti. We acknowledge the support of Amazon Web Services by making available the Rigetti Aspen-9 device using the Amazon Braket service. This research was funded by the Australian Research Council Centre of Excellence grant no. CE170100012, Laureate Fellowship no. FL150100019 and the Australian Government Research Training Program Scholarship. This work has been supported by the Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V. We gratefully acknowledge the financial support by the German Federal Ministry of Education and Research via ‘2D Nanomaterialien für die Nanoskopie der Zukunft’, FKZ no. 13XP5053A and the European Union, the European Social Funds and the Federal State of Thuringia under grant ID no. 2021FGI0043. This work was funded by the Deutsche Forschungsgemeinschaft (German Research Foundation) project no. 445275953. We acknowledge support by the German Space Agency DLR with funds provided by the Federal Ministry for Economic Affairs and Energy BMWi under grant no. 50WM2165 (QUICK3). D.W.B. is supported by Australian Research Council Discovery project nos. DP190102633 and DP210101367. C.D.M., I.P. and T.M. acknowledge funding from the EU H2020-FETFLAG-2018-03 under grant agreement no. 820495. We also acknowledge support by the Austrian Science Fund (FWF), through the SFB BeyondC (FWF project no. F7109) and the IQI GmbH, as well as the Office of the Director of National Intelligence, Intelligence Advanced Research Projects Activity, via US ARO grant nos. W911NF-16-1-0070 and W911NF-20-1-0007, and the US Air Force Office of Scientific Research via IOE grant no. FA9550-19-1-7044 LASCEM., Funder: Fraunhofer-Gesellschaft (Fraunhofer Organization); doi: https://doi.org/10.13039/501100003185, Funder: German Federal Ministry of Education and Research via ‘2D Nanomaterialien fur die Nanoskopie der Zukunft’, FKZ: 13XP5053A European Union, the European Social Funds and the Federal State of Thuringia under Grant ID 2021FGI0043 The authors acknowledge support by the German Space Agency DLR with funds provided by the Federal Ministry for Economic Affairs and Energy BMWi under grant number 50WM2165 (QUICK3)., Funder: EU H2020-FETFLAG-2018-03 under Grant Agreement no.820495 US Air Force Office of Scientific Research (AFOSR) via IOE Grant No. FA9550-19-1-7044 LASCEM., Funder: Amazon Web Services, Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer better sensitivity, per resource, than what can be achieved classically. However, to reach the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks, collective measurements, which generate entanglement between multiple copies of the quantum state, are necessary. Here, we experimentally demonstrate theoretically optimal single- and two-copy collective measurements for simultaneously estimating two non-commuting qubit rotations. This allows us to implement quantum-enhanced sensing, for which the metrological gain persists for high levels of decoherence, and to draw fundamental insights about the interpretation of the uncertainty principle. We implement our optimal measurements on superconducting, trapped-ion and photonic systems, providing an indication of how future quantum-enhanced sensing networks may look.