Generalized-mean Cramér-Rao bounds for multiparameter quantum metrology

Ma, Zhihao; Zhang, Chengjie

doi:10.1103/physreva.101.022303

Cited by 11 publications

(9 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In another work, Ref. [65] the authors present the difference between the regions of variances excluded by bounds on their arithmetic, geometric and harmonic means. What distinguishes our approach from the above works is that to obtain the trade-off curve we use the bound on the expected cost for a family of different costs all at once.…”

Section: Discussionmentioning

confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cramér-Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.Ever since its first formulation, the uncertainty principle has seen many refinements and clarifications. As quantum theory developed, its state-of-the-art concepts and mathematical tools were used to formulate in precise terms the ideas which were put forward in Heisenberg's 1927 paper [1]. As a result, our current understanding of the uncertainties inherent in quantum mechanics is spelled out in a collection of theorems pertaining to well defined operational tasks.Soon after Heisenberg's paper, rigorous proofs of his uncertainty relations were formulated [2][3][4]. Those are usually referred to as preparation uncertainty relations. Most well known is the relation due to Weyl and Robertson arXiv:2002.05961v1 [quant-ph]

show abstract

Section: Discussionmentioning

confidence: 99%

Uncertainty and trade-offs in quantum multiparameter estimation

Kull¹,

Guérin²,

Verstraete³

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…where the first equality can always be attained via the maximal likelihood estimation [4,57,58]. Thus, the precision of an estimation scheme with a given measurement is measured by…”

Section: Model and Basic Theorymentioning

confidence: 99%

Two-parameter estimation with three-mode NOON state in a symmetric triple-well potential

Yao¹,

Du²,

Hu³

et al. 2022

Commun. Theor. Phys.

View full text Add to dashboard Cite

We propose a scheme to realize two-parameter estimation via a Bose-Einstein condensates confined in a symmetric triple-well potential. The three-mode NOON state is prepared adiabatically as the initial state. The two parameters to be estimated are the phase differences between the wells.The sensitivity of this estimation scheme is studied by comparing quantum and classical Fisher information matrices. As a result, we find an optimal particle number measurement method. Moreover, the precision of this estimation scheme behaves the Heisenberg scaling under the optimal measurement.

show abstract

“…2, Eq. ( 12) gives the most informative lower bound on the estimation error, compared with the error bounds that was previously investigated [3,5,6,34].…”

mentioning

confidence: 99%

“…Therefore, the characterization of the quantum-limited bound on the estimation errors is of great importance to many practical applications of quantum estimation. Nevertheless, it is still challenging to derive, characterize, and understand the quantum limit on accuracies for the multiparameter estimation [9,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation

Lu,

Wang

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The quantum multiparameter estimation is very different with the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible, they cannot be jointly performed. We find a correspondence relationship between the inefficiency of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations. Taking this correspondence relationship as a bridge, we incorporate Heisenberg's uncertainty principle into quantum multiparameter estimation by giving a tradeoff relation between the measurement inefficiencies for estimating different parameters. For pure quantum states, this tradeoff relation is tight, so it can reveal the true quantum limits on individual estimation errors in such cases. We apply our approach to derive the tradeoff between attainable errors of estimating the real and imaginary parts of a complex signal encoded in coherent states and obtain the joint measurements attaining the tradeoff relation. We also show that our approach can be readily used to derive the tradeoff between the errors of jointly estimating the phase shift and phase diffusion without explicitly parameterizing quantum measurements.

show abstract

Generalized-mean Cramér-Rao bounds for multiparameter quantum metrology

Cited by 11 publications

References 53 publications

Uncertainty and trade-offs in quantum multiparameter estimation

Uncertainty and trade-offs in quantum multiparameter estimation

Two-parameter estimation with three-mode NOON state in a symmetric triple-well potential

Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation

Contact Info

Product

Resources

About