# Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation
## 6 Some Final Considerations about Benchmarking, Decoherence Effects, and Fidelity
### Fidelity and Possible Decoherence Effects Due to the Environment  
Technical implementations for security protocols involving quantum processing, as the current one, will depend strongly on the physical system where it pretends to be implemented. Quantum decoherence due to the interaction with the environment differently affects setups settled on photonic systems than matter systems. While photonic implementations are recommended whenever quantum information should not be stored. Despite quantum processing is commonly settled on gates models, all of them finally involve or reduce to physical interactions ruled by a Hamiltonian. For matter, the preferred approach to analyse such decoherence are the quantum open systems equations as Linblad or Redfield ones [59]. A simpler but none-less useful approach is the modelling of decoherence through non-Hermitian Hamiltonians [60]. Still, both approaches can become complex if a large number of gates are involved.  
Thus, quantum decoherence is the main challenge to reach scalability and reliability. In addition, it is known that decoherence effects (dephasing, amplitude, and depolarizing) increase harmfully the QBER to undesired effects near from the security bound [57]. A precise quantification about the fidelity of such systems is complex because it depends on the type and size of the gate and its architecture; also, on the number and kind of the quantum states involved, particularly those involving entanglement. For these reasons, together with the development of quantum information and its processing, this problem has been tackled through practical considerations for different implementations on matter and for the most typical gates [61]. While for photonic implementations decoherence becomes mild, it is not true for matter systems. Thus, gates as \(NOT\), Hadamard, \(C^{\ast}NOT_{b}\), Toffoli, and so forth, all of them involved in the current procedure, have been recently analysed for Nuclear Magnetic Resonance (NMR) using the Lindblad equation to give certain guidelines to quantum circuit designers about the decoherence for the most typical gates, thus reporting their fidelity behavior [62]. Such analysis shows as expected, that the decoherence process and the further loss of fidelity depend on the input state and the type of decoherence. By analyzing amplitude and phase damping as the most representative examples of noise, several aspects arise in the analysis: (a) deeper circuits (circuits with more gates) of course exhibit lower fidelity, (b) multiqubit gates do not necessarily show lower fidelity than single qubit ones, and (c) shorter time-scales to reach each gate still maintain fidelities near to one. For Noisy Intermediate Scale Quantum (NISQ) technologies, global coherence times are in the range of 50-100 \(\upmu\)s. Dealing with fidelities routinely implemented above 0.99 for single qubits gates, but also many two qubits gates. While, individual operation times are in the order of nanoseconds, so large circuits can be addressed during the entire coherence times [63]. Thus, circuits containing tens of gates are currently able to be implemented. Table 4 accounts for the gates and their barely type arranged by process (DT for double teleportation and PP for post-processing) and the number of qubits involved. More than half are single qubits gates, showing that the implementation on matter-based technologies is in order.