# Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation
## 2 Introductory Remarks for Contemporary Post-Quantum Cryptography  
Quantum cryptography is the science that pretends to exploit any quantum mechanical feature to perform cryptography tasks, which means methods of encryption naturally using the properties of quantum mechanics to secure and transmit data without hacking. The economy in quantum cryptography has been pursued through the main original developments despite the contemporary technology at the time those works were published. Possibly, QKD is the most important contribution to quantum cryptography by promoting the fusion of classical and quantum approaches, setting a natural incubator in which to develop the field.  
The first quantum protocol for QKD was the BB84 one [11] based on quantum conjugate variables. Such protocol states a procedure to state a key in the form of a chain of zeroes and ones without a direct transmission from the sender to the receiver. Instead, the key is codified through a series of quantum resources randomly prepared by the sender on one from two orthogonal agreed bases. Then, they are stochastically found by the receiver through random measurements on such bases. In the end, the bases used are shared by both parts to conserve the identical outcomes when the bases meet. Such a procedure allows us to detect eavesdropping when it intermediately alters the coincident bases and outcomes through a different basis measurement.  
Thus, QKD protocols, as that mentioned before, first used quantum correlations to set a quantum key between two parties (another one similar is the B92 [12]). Soon, other protocols appeared exploiting the statistical nature of quantum systems involved, as in the SARG04 [13]. While alternative protocols such as the E91 [14] used entanglement pairs more than just the quantum nature of states in terms of orthogonal basis in a symmetrical treatment of information to construct the key together. Moreover, Quantum Key Agreement (QKA) protocols [31] introduced a shared decision generation for the key.  
When quantum computers are introduced to break quantum codes of such developments, the scenario was moved to secure protocols including quantum computer-based attacks. It has raised the post-quantum cryptography terrain to set secure protocols against quantum computer attacks. Despite this, the roadmap is unclear because some of the most current classical symmetric cryptographic protocols are still considered to be relatively secure against quantum computer attacks [32], thus it is believed that classical approaches in theoretical cryptography could be combined with quantum cryptography trends [33].  
The current development introduces some elements exploiting quantum processing together with extreme features of quantum information as double teleportation, non-local operations performed via entanglement, and controlled measurements by quantum machines. Some features of the protocol also combine QKA approaches. Thus, they allocate the current proposal in the terrain of post-quantum cryptography (or quantum-safe cryptography) to set a QKD procedure reducing the eavesdropper success.  
Other technology concerns should be considered because of the growing complexity of the post-quantum protocols including more complex processing and finer theoretical cryptography considerations. Such aspects are similar to those premises considered in quantum processing: quality and reliability on state generation processes, development of coherent quantum gates to preserve their supposed quantum nature, and faithfully quantum measurement. Those aspects are remarked through the development.