Verifying the quantumness of a channel with an untrusted device

Abstract

Suppose one wants to certify that a quantum channel is not entanglement-breaking. I consider all four combinations of trusted and untrusted devices at the input and output of the channel, finding that the most interesting is a trusted preparation device at the input and an untrusted measurement device at the output. This provides a time-like analogue of EPR-steering, which turns out to reduce to the problem of joint measurability, connecting these concepts in a different way to other recent work. I suggest a few applications of this connection, such as a resource theory of incompatibility. This perspective also sheds light on why the BB84 key distribution protocol can be secure even with an untrusted measuring device, leading to an uncertainty relation for arbitrary pairs of ensembles.

7+1 pages. v2: Various clarifications, esp. in QKD section. To appear in JOSA B special issue "80 years of Steering and the Einstein-Podolsky-Rosen Paradox"

References in corpus (7)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Semi-device-independent security of one-way quantum key distribution
• Joint measurability of generalized measurements implies classicality
• Channel Steering
• Tight asymptotic key rate for the BB84 protocol with local randomisation and device imprecisions

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• Every quantum helps: Operational advantage of quantum resources beyond convexity
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• The future of secure communications: device independence in quantum key distribution
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Towards the device-independent certification of a quantum memory
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• Joint-measurability and quantum communication with untrusted devices
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• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Calibration-Independent Certification of a Quantum Frequency Converter
• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light
• A Note on Hierarchy of Quantum Measurement Incompatibilities
• On compatibility of binary qubit measurements
• Barycentric decomposition for quantum instruments
• Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations
• Semi-device-independent certification of high-dimensional quantum channels
• Quantifying incompatibility of quantum measurements through non-commutativity