# Markovian approximation for teleportation? [closed]

Assume a model including a system with time dependent Hamiltonian ( 3 entangled qubits subject to a noisy reservoir) coupled weakly to a thermal bath. in order to study the time evolution of a system I should derive master equations which describe the time evolution of reduced density matrix of a system. for this purpose we use Markov and rotating wave approximation which leads to master equation in Lindblad form. the Markov approximation is employed involving three main assumptions:

1. .The quantum system and the bath are uncorrelated, such that $\hat{\rho}(t)=\hat{\rho}S(t)\otimes\hat{\rho}B$.
2. The bath correlation functions decay much faster as compared to the system’s relaxation rate and internal dynamics.
3. The state of the bath is assumed to be a thermal stationary state.

which we know Markovian system is memory-less. with respect to these, we want to add teleportation process to this model and find the fidelity, this means we want to teleport information. In this case is that correct to use Markov approximation? do we need memory for teleportation? or we must use non-Markov approximation?

## closed as unclear what you're asking by Norbert Schuch, Jon Custer, sammy gerbil, Sebastian Riese, glSJul 23 '18 at 21:06

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• The Markov approximation governs the relation of the system and the bath. Teleportation only directly involves degrees of freedom of the system, in the limit case that the coupling to the bath gets infinitely weak the Lindblad master equation reduces to the von Neumann equation and we can describe teleportation as usual. The only difference when we couple to the bath is that there is dissipation, so that teleportation will not succeed always (because the coherence of our qubit states decay). To describe this decay of coherence the Markov approximation is sufficient. – Sebastian Riese Jul 20 '18 at 10:11
• When an open quantum system, due to its coupling with the external environment, continuously loses information to its surroundings, the noise induced dynamics is called Markovian. Non-Markovian quantum dynamics with memory effects arise when the system does not only lose information, but temporarily recovers some of it from the environment at a later time. in this case the point is the role of memory. I meant is that necessary for teleportation process , to have memory or not ? if is needed, can't we use markov approximation to derive the master equation? – S.CH Jul 22 '18 at 12:33
• I know what the terms mean, read my comment again: Teleportation works for closed quantum systems so you do not need an environment with a memory. Some dissipative bath will of course reduce the probability of successful teleportation (no matter whether in Markov approximation or not)! Of course you need some outside apparatus to communicate classical information, but this is not the noisy environment your task is about. – Sebastian Riese Jul 22 '18 at 15:57