Criteria for unbiased estimation: applications to noise-agnostic sensing and quantum channel estimation

Understand

We establish the necessary and sufficient conditions for {local} unbiased estimation in multi-parameter estimation tasks.

• More specifically, we first consider quantum state estimation, where multiple parameters are encoded in a quantum state, and derive simple and intuitive necessary and sufficient conditions for a {local} unbiased estimation based on the derivatives of the encoded state.
• To demonstrate the utility of our framework, we consider phase estimation under unknown Pauli noise.
• We show that while {local} unbiased phase estimation is infeasible with a naive scheme, employing an entangled probe with a noiseless ancilla enables local unbiased estimation.