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

Cited by in corpus (2)

• Incompatibility of quantum channels
• A Note on Hierarchy of Quantum Measurement Incompatibilities