We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes.

Quantum Bell nonlocality is an important quantum phenomenon. Recently, the shareability of Bell nonlocality under unilateral measurements has been widely studied. In this study, we consider the shareability of quantum Bell nonlocality under bilateral measurements. Under a specific class of projection operators, we find that quantum Bell nonlocality cannot be shared for a limited number of times, as in the case of unilateral measurements. Our proof is analytical and our measurement strategies can be generalized to higher dimension cases.