Verifying the quantumness of a channel with an untrusted device

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. (C) 2015 Optical Society of America