Estimation of Phase and Diffusion: Combining Quantum Statistics and Classical Noise

Knysh, Sergey; Durkin, Gabriel A.

doi:10.48550/arxiv.1307.0470

Cited by 22 publications

(33 citation statements)

References 33 publications

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“…So far the analysis of noisy measurement schemes was limited only to schemes governed by linear generators leading to some very pessimistic results [12][13][14][15][16][17][18][19]. Although, under certain circumstances such as the presence of non-Markovian environments [20,21], or frequency estimation with transversal noise [22], some improvement in the precision with respect to the shot-noise limit can be observed.…”

Section: Introductionmentioning

confidence: 99%

Precision bounds for noisy nonlinear quantum metrology

Zwierz

Wiseman

2014

Phys. Rev. A

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We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon loss and phase diffusion. We find that the second-order estimation scheme is affected by both types of noise in an analogous way as the linear one. Moreover, we observe that for both types of noise the gain in the phase sensitivity with respect to the linear estimation scheme is given by a multiplicative term O(1/N ). Interestingly, we also find that under certain circumstances, a careful engineering of the environment can, in principle, improve the performance of measurement schemes affected by phase diffusion.

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Section: Introductionmentioning

confidence: 99%

Precision bounds for noisy nonlinear quantum metrology

Zwierz

Wiseman

2014

Phys. Rev. A

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“…Nevertheless, the derivation of L θ is highly dependent on the structure of the density operator ρ(θ) and its parametrization. For several special cases, the analytical solution of L θ can be found, involving some mathematical tricks [36][37][38][39].…”

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confidence: 99%

Multiple phase estimation for arbitrary pure states under white noise

Yao

Xing

et al. 2014

Phys. Rev. A

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In any realistic quantum metrology scenarios, the ultimate precision in the estimation of parameters is limited not only by the so-called Heisenberg scaling, but also the environmental noise encountered by the underlying system. In the context of quantum estimation theory, it is of great significance to carefully evaluate the impact of a specific type of noise on the corresponding quantum Fisher information (QFI) or quantum Fisher information matrix (QFIM). Here we investigate the multiple phase estimation problem for a natural parametrization of arbitrary pure states under white noise. We obtain the explicit expression of the symmetric logarithmic derivative (SLD) and hence the analytical formula of QFIM. Moreover, the attainability of the quantum Cramér-Rao bound (QCRB) is confirmed by the commutability of SLDs and the optimal estimators are elucidated for the experimental purpose. These findings generalize previously known partial results and highlight the role of white noise in quantum metrology. Quantum metrology, emerged as a new branch of quantum technologies, provides a powerful and versatile framework for both theoretical and experimental studies in the field of quantum-enhanced parameter estimation [1][2][3][4]. However, any realistic physical system will suffer from various environmental noises via the coupling with its surroundings [5]. As pointed out in Ref.[4], analysis of the effects of noise is one of the major burgeoning trends of this field. With the efforts of multiple authors, it is clearly evident that even a very low noise level can destroy the quadratic improvement over the classical shot-noise limit [7][8][9][10]. Although a unified method to deal with noise of arbitrary form is still lacking, more in-depth study in this respect is continuing and the scope is far beyond the usual noisy quantum channels raised in [9,10]. In fact, a plenty variety of significant physical effects or processes can also be regarded as the corresponding noisy quantum channels in the context of quantum information theory. For instance, quite recently it is demonstrated that the relativistic effect and quantum cloning machines are excellent platforms for investigating the quantum feature of quantum metrology scenarios [11][12][13][14][15][16].On the other hand, due to the quantum Cramér-Rao inequality, quantum Fisher information (QFI) is recognized as the key quantity to characterize the ultimate precision in parameter estimation scenarios [17][18][19][20]. Therefore, a great amount of research work of noisy quantum metrology can be translated into the evaluation of the dynamics of QFI in the presence of a certain kind of noise. Though different kinds of upper bounds on QFI * Electronic address: xgwang@zimp.zju.edu.cn † Electronic address: cpsun@csrc.ac.cn have been obtained for various purposes [9,10,[21][22][23][24][25], the analytical treatment of QFI is usually a difficult task.To summarize, we realize that all these analytical approaches in the literature can be classified into the following three categories.

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“…For an example, it is worthwhile to analyze the robustness against the environment effects. Therefore, it is vital to explore the effects to the measurement precision in the presence of decoherence, 81,111,169,[210][211][212][213][214][215] temperature, 216 and particle losses. 99,138,[217][218][219][220] Besides to the metrology schemes using entanglement as a resource for beating the SQL, there are some alternative entanglement-free schemes beating the SQL.…”

Section: Summary and Discussionmentioning

confidence: 99%

Quantum Metrology With Cold Atoms

Huang

Zhong

et al. 2014

Annual Review of Cold Atoms and Molecules

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Quantum metrology is the science that aims to achieve precision measurements by making use of quantum principles. Attribute to the well-developed techniques of manipulating and detecting cold atoms, cold atomic systems provide an excellent platform for implementing precision quantum metrology. In this chapter, we review the general procedures of quantum metrology and some experimental progresses in quantum metrology with cold atoms. Firstly, we give the general framework of quantum metrology and the calculation of quantum Fisher information, which is the core of quantum parameter estimation. Then, we introduce the quantum interferometry with single and multiparticle states. In particular, for some typical multiparticle states, we analyze their ultimate precision limits and show how quantum entanglement could enhance the measurement precision beyond the standard quantum limit. Further, we review some experimental progresses in quantum metrology with cold atomic systems.

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Estimation of Phase and Diffusion: Combining Quantum Statistics and Classical Noise

Cited by 22 publications

References 33 publications

Precision bounds for noisy nonlinear quantum metrology

Precision bounds for noisy nonlinear quantum metrology

Multiple phase estimation for arbitrary pure states under white noise

Quantum Metrology With Cold Atoms

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