Experimental estimation of the quantum Fisher information from randomized measurements

Yu, Min; Li, Dongxiao; Wang, Jingcheng; Chu, Yaoming; Yang, Pengcheng; Gong, Musang; Goldman, Nathan; Cai, Jianming

doi:10.1103/physrevresearch.3.043122

Cited by 35 publications

(17 citation statements)

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“…Measurement is critical in quantum parameter estimation [112][113][114][115]. On one hand, all asymptotic bounds require some optimal measurements to attain if it is at- tainable, and hence the search of optimal measurements is a natural requirement in theory to approach the ultimate precision limit.…”

Section: Measurement Optimizationmentioning

confidence: 99%

QuanEstimation: an open-source toolkit for quantum parameter estimation

Zhang¹,

Yu²,

Yuan³

et al. 2022

Preprint

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Quantum parameter estimation promises a high-precision measurement in theory, however, how to design the optimal scheme in a specific scenario, especially under a practical condition, is still a serious problem that needs to be solved case by case due to the existence of multiple mathematical bounds and optimization methods. Depending on the scenario considered, different bounds may be more or less suitable, both in terms of computational complexity and the tightness of the bound itself. At the same time, the metrological schemes provided by different optimization methods need to be tested against realization complexity, robustness, etc. Hence, a comprehensive toolkit containing various bounds and optimization methods is essential for the scheme design in quantum metrology. To fill this vacancy, here we present a Python-Julia-based open-source toolkit for quantum parameter estimation, which includes many well-used mathematical bounds and optimization methods. Utilizing this toolkit, all procedures in the scheme design, such as the optimizations of the probe state, control and measurement, can be readily and efficiently performed.

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Section: Measurement Optimizationmentioning

confidence: 99%

QuanEstimation: an open-source toolkit for quantum parameter estimation

Zhang¹,

Yu²,

Yuan³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Motivated by these developments, the quantum metric was experimentally measured in several quantum-engineered systems, including cold atoms in optical lattices [28], NV centers in diamond [29][30][31], exciton polaritons [32] and superconducting qubits [33,34]. The generalization of the quantum metric to mixed states (also known as the Bures metric) was also recently estimated through randomized measurements [35].…”

Section: Introductionmentioning

confidence: 99%

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

2022

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Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:~the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties can, in special cases, be deduced from the quantum metric. In this work, we establish general and exact relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. In particular, we demonstrate that topological indices (Chern numbers or winding numbers) are bounded by the quantum volume determined by the quantum metric. Our theoretical framework, which builds on the Clifford algebra of Dirac matrices, is applicable to topological insulators and semimetals of arbitrary spatial dimensions, with or without chiral symmetry. This work clarifies the role of the Fubini-Study metric in topological states of matter, suggesting unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.

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“…Specifically, the precision limit for single parameter estimation is given by the quantum Cramér-Rao bound (CRB) [1], which relates the smallest achievable variance of an unbiased estimator to the inverse of the QFI of the underlying state. The QFI was measured in various experiments by using different methods [16][17][18][19][20][21]. While recent experiments tested and verified the CRB through QFI measurements in the context of single-parameter-evaluation schemes [21], the extension to multi-parameter scenarios is generally more complex due to the possible incompatibility of optimal quantum measurements targeting each parameter [22][23][24][25][26][27][28][29][30][31][32].…”

mentioning

confidence: 99%

“…where N represents the number of measurements. To verify the above geometric (Berry-curvature) bound, we experimentally extract the full quantum geometric tensor (QGT) by measuring the fidelity between neighbouring quantum states in parameter space [19,44]. In Fig.…”

mentioning

confidence: 99%

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Experimental demonstration of topological bounds in quantum metrology

Yu¹,

Li²,

Chu³

et al. 2022

Preprint

Self Cite

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Experimental estimation of the quantum Fisher information from randomized measurements

Cited by 35 publications

References 50 publications

QuanEstimation: an open-source toolkit for quantum parameter estimation

QuanEstimation: an open-source toolkit for quantum parameter estimation

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

Experimental demonstration of topological bounds in quantum metrology

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