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It is well known that certain quantum correlations like quantum steeringexhibit a monogamous relationship. In this paper, we exploit the asymmetricnature of quantum steering and show that there exist states which exhibit apolygamous correlation, known as collective correlation [He and Reid, Phys.Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can besteered only by the joint effort of the other two parties, Bob and Charlie. Asan example, we explicitly single out a particular set of $3$ qubit states whichexhibit this polygamous relationship, known as collective steerability. Weprovide a recipe to identify the complete set of such states. We also provide apossible application of such states to an information theoretic task, termed asquantum key authentication (QKA) protocol. QKA can also be used in conjunctionwith other well known cryptography protocols to improve their security and weprovide one such example with quantum private comparison (QPC).

Authentication protocol based on collective quantum steering