Memory Effects in Quantum Metrology

Quantum metrology concerns estimating a parameter from multiple identical uses of a quantum channel. We extend quantum metrology beyond this standard setting and consider the 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 4. 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.