A Contextuality Based Quantum Key Distribution Protocol

Abstract

In 2005 R. Spekkens presented a generalization of noncontextuality that applies to imperfect measurements (POVMs) by allowing the underlying ontological model to be indeterministic. Unlike traditional Bell-Kochen-Specker noncontextuality, ontological models of a single qubit were shown to be contextual under this definition. Recently, M. Pusey showed that, under certain conditions, exhibiting an anomalous weak value implies contextuality. We will present a single qubit prepare and measure QKD protocol that uses observation of anomalous weak values of particular observables to estimate the quantum channel error rate and certify the security of the channel. We will also argue that it is the “degree” of contextuality of the noisy qubits exiting the channel that fundamentally determine the secure key rate. A benefit of this approach is that the security does not depend on the fair sampling assumption, and so is not compromised by Eve controlling Bob’s measurement devices. Thus it retains much of the benefit of “Measurement Device Independent” QKD protocols while only using single photon preparation and measurement.