Parallelization and factorization in quantum metrology Abstract: Quantum Metrology is the study of the ultimate precision allowed by quantum theory to the estimation of physical parameters. In the typical scenario, the parameter of interest labels the physical transformation implemented by a black box and the problem is to find the best strategy to estimate the parameter using a finite number N of queries to the black box. In this context, quantum theory offers an advantage over classical estimation in several cases, an advantage that is often described in the Cramér-Rao approach as a reduction of the statistical error with respect to the case where N independent measurements are performed. In this talk I will argue that in all these examples the key difference between quantum and classical estimation consists in the fact that the different queries to the black box can be performed in parallel, rather then in a sequence. Once emphasized the importance of parallelization as a distinctive treat of Quantum Metrology I will present a sufficient condition that ensures the parallelizability of the optimal estimation strategy. Moreover, I will discuss the closely related problem of factorization, namely the question whether the optimal estimation of independent parameters can be achieved by independent estimation strategies. In this case, I will present a general theorem that ensures the factorization of the optimal network for estimation in a large number of cases. The result uses a semidefinite programming technique by Mittal and Szegedy in combination with the theory of quantum combs, a convenient operator framework for the optimization of quantum networks. Biography: Giulio Chiribella is currently an Associate Professor at Institute for Interdisciplinary Information Sciences, Tsinghua University. He obtained his PhD at Pavia University under the supervision of Professor Giacomo Mauro D'Ariano. From 2006 to 2009 he has been a postdoctoral fellow of the Quantum Information Group at Pavia University. |