Reliable Entanglement Verification

Abstract

Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by M. Christandl and R. Renner to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements nor the assumption of an independent and identically distributed (i.i.d.) source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.

13 pages, 8 figures

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• Entanglement detection
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• Entanglement detection in hybrid optomechanical systems
• On experimental procedures for entanglement verification
• Experimental bound entanglement in a four-photon state
• Multipartite entanglement detection via structure factors
• Certifying experimental errors in quantum experiments
• Entanglement verification with finite data
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• Accessible nonlinear entanglement witnesses
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• Witnessing the non-classical nature of gravity in the presence of unknown interactions
• Practical, Reliable Error Bars in Quantum Tomography
• Single-copy entanglement detection
• Experimental few-copy multi-particle entanglement detection
• Entanglement Witnesses for Indistinguishable Particles
• High posterior density ellipsoids of quantum states
• Entanglement Verification in Quantum Networks with Tampered Nodes
• Quantum Model Averaging
• Beating detection loophole in nonlinear entanglement witnesses
• Valid and efficient entanglement verification with finite copies of a quantum state
• Measurement-device-independent nonlinear entanglement witnesses
• Experimental Verification of Entangled States in the Adversarial Scenario
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses