Many future quantum technologies rely on the generation of entangled states. Quantum devices will require verification of their operation below some error threshold, but the reliable detection of quantum entanglement remains a considerable challenge for large-scale quantum systems. Well-established techniques for this task rely on the measurement of expectation values of entanglement witnesses; however these require many measurement settings to be extracted. Here, we develop a generic framework for efficient entanglement detection that translates any entanglement witness into a resource-efficient probabilistic scheme, whose confidence grows exponentially with the number of individual detection events, namely copies of the quantum state. To benchmark our findings, we experimentally verify the presence of entanglement in a photonic six-qubit cluster state generated using three single-photon sources operating at telecommunication wavelengths. We find that the presence of entanglement can be certified with at least 99.74% confidence by detecting 20 copies of the quantum state. Additionally, we show that genuine six-qubit entanglement is verified with at least 99% confidence by using 112 copies of the state. Our protocol can be carried out with a remarkably low number of copies and in the presence of experimental imperfections, making it a practical and applicable method to verify large-scale quantum devices.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.
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The authors thank I. Alonso Calafell for help with the detectors and T. Strömberg for helpful discussions. V.S. acknowledges support from the University of Vienna through the Vienna Doctoral School. A.D. acknowledges support from project no. ON171035 of the Serbian Ministry of Education and Science and from the scholarship awarded from The Austrian Agency for International Cooperation in Education and Research (OeAD-GmbH). L.A.R. acknowledges support from the Templeton World Charity Foundation (fellowship no. TWCF0194). P.W. acknowledges support from the European Commission through ErBeStA (no. 800942), from the Austrian Science Fund (FWF) through CoQuS (W1210-N25), BeyondC (F7113-N38) and NaMuG (P30067-N36), the US Air Force Office of Scientific Research (FA2386-232 17-1-4011), the Austrian Research Promotion Agency (FFG) through the QuantERA ERA-NET Cofund project HiPhoP, and Red Bull. B.D. acknowledges support from the Foundational Question Institute (FQXi) grant FQXi-MGA-1806 and from an ESQ Discovery Grant of the Austrian Academy of Sciences.
The authors declare no competing interests.
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