  Quantum metrology concerns estimating a parameter from multiple identical
uses of a quantum channel. We extend quantum metrology beyond this standard
setting and consider estimation of a physical process with quantum memory, here
referred to as a parametrized quantum comb. We present a theoretic framework of
metrology of quantum combs, and derive a general upper bound of the comb
quantum Fisher information. The bound can be operationally interpreted as the
quantum Fisher information of a memoryless quantum channel times a dimensional
factor. We then show an example where the bound can be attained up to a factor
of four. With the example and the bound, we show that memory in quantum sensors
plays an even more crucial role in the estimation of combs than in the standard
setting of quantum metrology.
