Markovian

import Quantum_channel

def CP_divisible [quantum_channel 𝒩] :=
∀ 0 ≤ s ≤ t, E(t,0) = E(t,s) ◦ E(s,0) ∧ completely_positive E(t,s)

def Markovian := CP_divisible

• “A characteristic of non-Markovian evolutions: divisibility of the evolution in CP maps is not enough to transform the evolution from non-Markovian to Markovian.”

• non-Markovianity and channel memory;

  • information backflow: Information leaks from the system to the environment, stays in the environment’s memory, then returns to the system;

  • “non-Markovian dynamics are associated with a backflow of information.

  • One of the common witnesses of this backflow of information is the distinguishability between two states.”

• Non-Markovianity boosts the efficiency of thermal biomolecular switches;

References

• Lautenbacher2021;