Universal quantum estimation

D. Bruss

Dagmar Bruß, ARTUR K. EKERT, Chiara Macchiavello

A. Hayashi, T. Hashimoto, M. Horibe

A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by Bruss and Macchiavello by establishing a connection to optimal quantum cloning. An explicit condition for POVM measurement operators for optimal estimators is obtained, by which we show optimal estimators with finite POVM exist but not generally universal, where universality means the fidelity is independent of input states. However any optimal estimator for M(>N) copies is universal if it is used for N copies as input.

François Chapeau‐Blondeau

Yu Watanabe

Jieci Wang, Zehua Tian, Jiliang Jing +1 more

We study the parameter estimation for excitations of Dirac fields in the expanding Robertson–Walker universe. We employ quantum metrology techniques to demonstrate the possibility for high precision estimation for the volume rate of the expanding universe. We show that the optimal precision of the estimation depends sensitively on the dimensionless mass m˜ and dimensionless momentum k˜ of the Dirac particles. The optimal precision for the ratio estimation peaks at some finite dimensionless mass m˜ and momentum k˜. We find that the precision of the estimation can be improved by choosing the probe state as an eigenvector of the hamiltonian. This occurs because the largest quantum Fisher information is obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.