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.