Authentication protocol based on collective quantum steering

It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of three qubit states which exhibit this polygamous relationship, known as collective steerability. We provide a recipe to identify the complete set of such states. We also provide a possible application of such states to an information theoretic task, termed as quantum key authentication (QKA) protocol. QKA can also be used in conjunction with other well-known cryptography protocols to improve their security, and we provide one such example with quantum private comparison.

Figure 1

Plot of the left-hand side of Eq. (4) considering Pauli bases with respect to arbitrary reference frame (see the Appendix) vs $\alpha$ for generalized GHZ state in Eq. (9). For this range of $\alpha$ under the curve, inequality (4) shows violation.