Question

Is the Identity a markovian or non-markovian transformation?

Answer 1

I'm working under the framework of quantum operations. If I understand it right, a map which is completely positive and trace preserving should represent a markovian process. Furthermore, I've read that unitary evolution of a system is trivially markovian.


For all these reasons, I expect that identity map should be a markovian process, since it is completely positive, trace-preserving and of course it is unitary. But, on the other hand, If I apply the identity on a state, it remains the same, so the "memory" of the process should be maximal; despite how many times the map is applied, the initial state is kept unchanged, so it should be a non-markovian process... I probably have a confusion in concepts or definitions, could someone please make it clear? Thanks in advance.

Answer 2

For all these reasons, I expect that identity map should be a markovian process, since it is completely positive, trace-preserving and of course it is unitary. But, on the other hand, If I apply the identity on a state, it remains the same, so the "memory" of the process should be maximal; despite how many times the map is applied, the initial state is kept unchanged, so it should be a non-markovian process... I probably have a confusion in concepts or definitions, could someone please make it clear? Thanks in advance.