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Optimal Local Measurements in Single-Parameter Quantum Metrology by Liu, Jia-Xuan; Yang, Jing; Shi, Hai-Long; Yu, Sixia is a scholarly article available to read on EtoBox.

What is Optimal Local Measurements in Single-Parameter Quantum Metrology about?

Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of locality in quantum measurements must be considered. In this work, we investigate the possibility of achieving the Quantum Cram\'er-Rao Bound (QCRB) through local measurements (LM). We first demonstrate that if there exists a LM to saturate the QCRB for qubit systems, then we can construct another rank-1 local projective measurement to saturate the QCRB. In this sense, rank-1 local projective measurements are sufficient to analyze the problem of saturating the QCRB. For pure qubits, we propose two necessary and sufficient methods to determine whether and how a given parameter estimation model can achieve QCRB through LM. The first method, dubbed iterative matrix partition method (IMP) and based on unitary transformations that render the diagonal entries of a tracless matrix vanish, elucidates the underlying mathematical structure of LM as well as the local measurements with classical communications (LMCC), generalizing the result by [Zhou et al Quant

Author

Liu, Jia-Xuan; Yang, Jing; Shi, Hai-Long; Yu, Sixia

Published

2023

Language

EN