Uncertainty and Trade-offs in Quantum Multiparameter Estimation

Understand

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system.

• They quantify trade-offs in accuracy between complementary pieces of information about the system.
• In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators.
• This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit.