# Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation
## 5 A QKD Protocol Based on a Shared Collaboration among Three Parties  
Despite many cryptography developments for QKD having emerged since 1984 after the BB84 protocol, most of them to a large extent are based on it. By proposing modifications or alternative approaches, they have improved the security or efficiency, together to prevent more sophisticated kinds of attack, particularly those possibly coming from a quantum computer. Thus, some of them have received names by their authors, as it occurs in the area. Thus, BB84 based protocols are completely valid nowadays. Among the BB84-like protocols for QKD, we can find the six-state protocol [40] which, rather than using two or four states as in the BB84, uses six states on three bases \(\mathbf{X}\), \(\mathbf{Y}\) and \(\mathbf{Z}\), thus causing the eavesdropper to produce a higher rate of error. For the case of the SARG04 protocol [13], it shares the first step of photon transmission with BB84, but then, for the second step, [PERSON] does not directly announce her bases, but a pair of non-orthogonal states instead, one of which is being used to encode her bit. Another protocol, the BBM92 [41] coincides with BB84 in the fact that if [PERSON] possesses the source, then her measurement (which is led on a random basis) would prepare the state to be sent to [PERSON] in one of the four possible states of those used in the BB84, and there is no way of knowing whether [PERSON] first measured part of a Bell state or she prepared a qubit state using a random number generator. In [42], a simplified three-state BB84 protocol was presented. In this case, [PERSON] sends three possible states to [PERSON], but he performs a simplified measurement with a basis-independent detection efficiency condition, thus limiting an eavesdropper to control the efficiency of detection, depending on [PERSON]'s basis choice. Another approach, based on the BB84, is the protocol presented in [43], where both, sender and receiver, select a random basis for modulation, encode on basis of random bits. Thus, both send the qubits over a quantum channel to each other. Then, both decode on basis of their random bits. Finally, both exchange their random basis and correct the positions of common bits. This process allows both, sender and receiver, to get two keys and a final key can be generated by combining them. Another protocol is presented in [44], which is identical to the BB84 protocol for the entire quantum mechanism, but the difference is that such protocol uses private reconciliation from a random seed and asymmetric cryptography for the classic procedures. In another trend, Quantum Key Agreement (QKA) protocols (those whereby two or more parties agree upon a key over insecure communication channels based on their exchanged messages) which are based on the BB84 protocol [45], but the outcome of the protocol is going to be influenced by both parties. Therefore, no one can determine the shared key alone and the protocol has 50% qubit efficiency after the random sampling discussion and it provides unconditional security.  
In our current proposal, several parties meet to generate the quantum key but via teleportation, entanglement, and collaboration, thus reducing the rate of success for an individual eavesdropper. At this point in our development, we have shown the prescriptions to solve the control problem of post-selecting the states in the Alice/Bob\({}_{0}\) and Bob\({}_{1}\) subsystems. In such sense, [PERSON]/Bob\({}_{0}\) pretends, after [PERSON]\({}_{1}\) applies the transformation characterized by an agreed \(\omega_{1}\), to control the system configuration in possession of [PERSON]\({}_{1}\) (the control and the Bob\({}_{1}\) subsystem inclusively) to secretly reach one of the states \(|b_{j}\rangle\) in the control and to set one of the orthogonal states \(|0\rangle_{\theta,p},|1\rangle_{\theta,p}\) (note that this knowledge keeps unknown for him). In the following subsection, we will exploit this procedure to state the QKD scheme.