Multiple-parameter quantum estimation and measurement of nonselfadjoint observables

Yuen, Horace P.; Lax, M.

doi:10.1109/tit.1973.1055103

Cited by 234 publications

(308 citation statements)

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“…Quantum versions for inequalities under the smoothness assumptions, i.e., Quantum Cramér-Rao (QCR) inequality ( [12], [15], [24]) and Quantum Bhattacharyya (QB) inequality ( [5]), have already been studied a lot.…”

Section: Quantum Estimation Theory With Smoothness Assumptions (I)mentioning

confidence: 99%

“…We consider singular submodels of Gaussian state model, whose theory ( [24,15]) is reviewed in the next subsection. In last subsection of this section, we study a vector valued submodel of Gaussian state model, to see the effect of non-commutativity explicitly.…”

Section: Submodels Of Gaussian State Modelmentioning

confidence: 99%

“…Under these smoothness assumptions, tractable lower bounds to the MSE of the estimator had been studied, and some of them give achievable bounds ( [12,15,24]). Especially, in asymptotic regime, we have lots of results on achievable bounds.…”

Section: Introductionmentioning

confidence: 99%

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Quantum estimation for non-differentiable models

Tsuda¹,

Matsumoto²

2005

J. Phys. A: Math. Gen.

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State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use derivative of density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In the paper, lower bounds to a Mean Square Error (MSE) of an estimator are derived for a quantum estimation problem without smoothness assumptions. Our main idea is to replace the derivative by difference, as is done in classical estimation theory. We applied the inequalities to several examples, and derived optimal estimator for some of them.

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Section: Quantum Estimation Theory With Smoothness Assumptions (I)mentioning

confidence: 99%

Section: Submodels Of Gaussian State Modelmentioning

confidence: 99%

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Quantum estimation for non-differentiable models

Tsuda¹,

Matsumoto²

2005

J. Phys. A: Math. Gen.

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“…It was extended to a quantum mechanical formalism in the 1960's by Helstrom [9] and later by Yuen and Lax [28], see [10] for the rigorous version.…”

Section: Introductionmentioning

confidence: 99%

Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

Gibilisco

Hiai

Petz

2009

IEEE Trans. Inform. Theory

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In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given here considerably simplify the previously proposed proofs and leads to more general inequalities.2000 Mathematics Subject Classi cation. Primary 62B10, 94A17; Secondary 46L30, 46L60.

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“…The first papers dealing with quantum statistical problems appeared in the seventies [23,56,55,6,24] and tackled issues such as quantum Cramér-Rao bounds for unbiased estimators, optimal estimation for families of states possessing a group symmetry, estimation of Gaussian states, optimal discrimination between non-commuting states. In recent years there has been a renewed interest in the field [21,22,36,5] and the advances in quantum engineering have led to the first practical implementations of theoretical methods [1,16,43].…”

Section: Introductionmentioning

confidence: 99%

Local Asymptotic Normality in Quantum Statistics

Guţǎ

Jenčová

2007

Commun. Math. Phys.

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The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family ϕ n θ 0 +u/ √ n consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state φu of an algebra of canonical commutation relations. The convergence holds for all "local parameters" u ∈ R m such that θ = θ0 + u/ √ n parametrizes a neighborhood of a fixed point θ0 ∈ Θ ⊂ R m . In order to prove the result we define weak and strong convergence of quantum statistical experiments which extend to the asymptotic framework the notion of quantum sufficiency introduces by Petz. Along the way we introduce the concept of canonical state of a statistical experiment, and investigate the relation between the two notions of convergence. For reader's convenience and completeness we review the relevant results of the classical as well as the quantum theory.

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Multiple-parameter quantum estimation and measurement of nonselfadjoint observables

Cited by 234 publications

References 10 publications

Quantum estimation for non-differentiable models

Quantum estimation for non-differentiable models

Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations

Local Asymptotic Normality in Quantum Statistics

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