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FM: Fall Meeting

FM 24: Quantum Sensing: Entanglement and Beyond Shot Noise

FM 24.8: Talk

Montag, 23. September 2019, 18:15–18:30, 3044

Maximal quantum Fisher information for mixed states — •Lukas J. Fiderer¹, Julien M.E. Fraïsse², and Daniel Braun¹ — ¹Eberhard-Karls-University Tuebingen — ²Seoul National University

The optimal initial state for estimating a parameter encoded to the state through unitary dynamics has been known since long: an equal superposition of eigenstates corresponding to the largest and smallest eigenvalue of the generator of the unitary dynamics. In principle, such an optimal initial state can be prepared by applying an appropriate unitary transformation to an available pure state.

However, access to pure states is not always granted in realistic measurement setups, for instance, due to noise or interactions with an environment. In the present work, we answer the following question: Given a mixed state, what is the optimal initial state that can be prepared with the help of a unitary transformation?

We give the quantum Fisher information for this optimal initial state and extend results from Pang et al. for optimal quantum metrology with pure states and Hamiltonian control to the regime of mixed states. In particular, we prove that even from thermal states of arbitrary finite temperature we can prepare initial states that allow for Heisenberg scaling.