Abstract

Quantum sensing enables higher precision measurements in several applications when compared to classical sensors. This quantum advantage is typically characterized by the scaling of the quantum Fisher information (QFI) with respect to the number of qubits involved in the sensing. Heisenberg scaling (HS) refers to the quadratic improvement in QFI compared to the standard quantum limit (SQL) achievable with unentangled sensors. However, even when a quantum probe state enables such an advantage, noise can render the state useless in going beyond the SQL. In this talk, I will first consider the design of code-inspired probe states that can achieve HS in single-parameter magnetic field sensing under the presence of some qubit erasures. The setting is robust quantum metrology, where there is no active syndrome measurement or error correction performed. I will show that the QFI of the scheme is intrinsically determined by the variance of the weight distribution of the code. I will demonstrate how code concatenation makes the HS attainable under a limited number of erasures.

Next, I will consider the extension beyond erasures to qubit dephasing and ask if HS is still achievable. Here, I will show that the QFI depends on the weight enumerator of the dual code. Using this, I will show that HS cannot be achieved in magnetic field sensing under dephasing noise and more generally when the Hamiltonian and the noise are acting in the same Pauli basis. This extends the well-known Hamiltonian-Not-in-Lindblad-Span (HNLS) condition to robust metrology where there is no active quantum error correction. Overall, I will demonstrate that classical coding tools such as the weight enumerator directly lend insights into robust quantum metrology.

This is based on separate joint work with Yingkai Ouyang (paper) and Oskar Novak (paper).