Device-independent secure correlations in sequential quantum scenarios

Abstract

Device-independent quantum information is attracting significant attention, particularly for its applications in information security. This interest arises from the fact that the security of device-independent protocols does not depend on the internal workings of the devices, but rather on the observed outcomes of spatially separated measurements together with the validity of quantum theory. Sequential scenarios, i.e., where measurements occur in a precise temporal order, have been proved to enhance performance of device-independent protocols in some specific cases by enabling the reuse of the same quantum state. In this work, we propose a systematic approach to designing sequential quantum protocols for device-independent security. Our method begins with a bipartite self-testing qubit protocol and transforms it into a sequential protocol by replacing one measurement with a non-projective Positive Operator Valued Measurement (POVM) and adding an additional user thereafter. We analytically prove that, with this systematic construction, the resulting ideal correlations are secure in the sense that they cannot be reproduced as a statistical mixture of other correlations, thereby enabling, for example, the device-independent certification of all the randomness present in the observed correlations. The general recipe we provide can be exploited for further development of new device-independent quantum schemes for security.