  Mutual distance bounding (DB) protocols enable two distrusting parties to
establish an upper-bound on the distance between them. DB has been so far
mainly considered in classical settings and for classical applications,
especially in wireless settings, e.g., to prevent relay attacks in wireless
authentication and access control systems, and for secure localization. While
recent research has started exploring DB in quantum settings, all current
quantum DB (QDB) protocols employ quantum-bits (qubits) in the rapid-bit
exchange phase and only perform one-way DB. Specifically, the latest QDB
proposals improve the initial ones by adding resistance to photon number
splitting attacks, and improving round complexity by avoiding communication
from the prover to the verifier in the last authentication phase. This paper
presents two new QDB protocols that differ from previously proposed protocols
in several aspects: (1) to the best of our knowledge, our protocols are the
first to utilize entangled qubits in the rapid-bit exchange phase, previous
protocols relied on sending individual qubits, not those from a pair of
entangled ones; (2) our second protocol can perform mutual QDB between two
parties in one execution, previous QDB protocols had to be executed twice with
the prover and verifier roles reversed in each execution; (3) the use of
entangled qubits in our protocols thwarts attacks that previous QDB protocols
were prone to; (4) and finally, our protocols also eliminate the need for
communication from the prover to the verifier in the last authentication phase,
which was necessary in some previous QDB protocols. Our work paves the way for
several interesting research directions which we briefly discuss in detail in
the appendix.
