<i>N</i>-body-extended channel estimation for low-noise parameters

Hotta, Masahiro; Karasawa, Tokishiro; Ozawa, Masanao

doi:10.1088/0305-4470/39/46/015

Cited by 16 publications

(13 citation statements)

References 14 publications

(15 reference statements)

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“…A good candidate for a parameter invariant under local * Electronic address: amonras@ifae.es unitaries is the strength of a locally depolarizing channel, i.e., a tensor product of depolarizing channels which mimics the tensor structure that defines locality for the given parties. It has been noted that entanglement helps, as expected, in estimating the parameters of a quantum channel [8,9]. In the specific case of a two-qubit locally depolarizing channel, maximally entangled states achieve the best precision in the estimation for some range of depolarization.…”

mentioning

confidence: 76%

“…. Because of the 1/ǫ divergence in the frontier of pure states, a solution for Λ ǫ , for initial pure states, is [9]…”

Section: Pacs Numbersmentioning

confidence: 99%

“…The minimization performed by Eve will result in an expected QFI which immediately translates into Eq. (9). We proceed to note some properties of this entanglement measure.…”

Section: Pacs Numbersmentioning

confidence: 99%

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Operational Interpretation for Global Multipartite Entanglement

Boixo

Monràs

2008

Phys. Rev. Lett.

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We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.

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mentioning

confidence: 76%

“…. Because of the 1/ǫ divergence in the frontier of pure states, a solution for Λ ǫ , for initial pure states, is [9]…”

Section: Pacs Numbersmentioning

confidence: 99%

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Operational Interpretation for Global Multipartite Entanglement

Boixo

Monràs

2008

Phys. Rev. Lett.

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“…Moreover, the Cramér-Rao bound cannot be always attained even in O(ǫ 0 ). The disadvantage can be remedied by using the ancilla-extension of the low-noise channel [4]. In fact, the bound becomes attainable again when D ≤ N 2 − 1.…”

Section: Channel Estimationmentioning

confidence: 99%

“…The increase of the Fisher information due to the prior entanglement with non-local output measurement, which is called the ancilla-assisted enhancement, has been analyzed for the ancilla-extended version of the low-noise channel [1]. The low-noise channel has been also extended to the channel on the many-body system [4], and this work shows that the maximum of the Fisher information can be attained by a factorized input state.…”

Section: Introductionmentioning

confidence: 99%

Channel estimation theory of low-noise multiple parameters: Attainability problem of the Cramér-Rao bounds

Hotta

Karasawa

2008

Phys. Rev. A

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We consider the achievability problem of the Cramér-Rao bound for multiparameter estimations. In general, it is not achievable due to the noncommutativity of optimal measurements for the corresponding parameters. However, we show that, under certain conditions, it can always be attained up to the leading order in the parameters as long as D ഛ N − 1, where D and N denote the number of parameters and the dimension of the system, respectively. After proving that, we discuss the achievability in the context of channel estimation for a general channel called a low-noise channel, which is very useful for investigating parameter estimation in the leading order. This allows us to find an ancilla-assisted enhancement effect: if entangled input states with an ancilla system are utilized for the channel estimation together with collective measurements on those output states, the bound becomes achievable for D ഛ N 2 −1.

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Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation

Hayashi

2011

Commun. Math. Phys.

102

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In a unified viewpoint in quantum channel estimation, we compare the Cramér-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramér-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O( 1 n ). We also derive a sufficient condition for that the minimum mean square error decreases with the order O( 1 n ).Simpler estimation scheme of quantum channel different analyses were reported concerning asymptotic behavior of MSE. As the first case, in the estimations of depolarizing channels and Pauli channels, the optimal MSE behaves as O( 1 n ) [1,3]. As the second case, in the estimation of unitary, the optimal MSE behaves as O( 1 n 2 ) [4,5,6,7,8,9,10,11]. In the second case, two different types of results were reported: One is based on the Cramér-Rao approach [4,5]. The other is based on the mini-max approach [6,7,8,9,10,11].The Cramér-Rao approach is based on the notion of locally unbiased estimator, and allows one to give a simple lower bound (the Cramér-Rao bound) to the mean square error (MSE) at a given point. The mini-max approach aims to minimize the maximum of the MSE over all possible values of the parameter. The mini-max approach is more meaningful than the Cramér-Rao approach because the true value of the parameter is unknown. So, the Cramér-Rao bound is just Comparison between Cramer-Rao and mini-max approaches 3 a lower bound in general, while it can be asymptotically acheived in the case of quantum state estimation with the n copies of the unknown state. However, the Cramér-Rao bound has been considered so many times in the literatures [1,3,4,5]. The reason seems that computing the mini-max bound is a much harder problem. Indeed, there are only very few examples of calculations of the mini-max bound, and most of them are in the compact group covariant setting, in which, as was shown by Holevo [15], the mini-max bound coincides with the Bayesian average of the MSE over the normalized invariant measure. So, many researchers [6,7,8,9,10,11] applied this approach to quantum channel estimation under the group covariance. As the most simple case for unitary estimation, phase estimation has been treated with the mini-max approach by several papers [9,10,11], and it has been shown that the minimum MSE that behaves as O( 1 n 2 ). On the other hand, the Cramér-Rao approach suggests the noon state as the optimal input [36,37] in phase estimation. The later estimation scheme was experimentally demonstrated in the case of n = 4 [32,33]and n = 10 [34]. Also, another group [31] experimentally demonstrated an estimation protocol concerning the group covariant approach proposed by [35]. In phase estimation with group covariant framework, the asymptotic minimum MSE behaves as ...

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N-body-extended channel estimation for low-noise parameters

Cited by 16 publications

References 14 publications

Operational Interpretation for Global Multipartite Entanglement

Operational Interpretation for Global Multipartite Entanglement

Channel estimation theory of low-noise multiple parameters: Attainability problem of the Cramér-Rao bounds

Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation

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