Quantum Cramér-Rao bound for quantum statistical models with parameter-dependent rank

Ye, Yating

doi:10.1103/physreva.106.022429

Cited by 4 publications

(2 citation statements)

References 35 publications

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“…Similarly, if we want to estimate a rotation about the y -axis only any state with

will be optimal, except when

is exactly equal to 0 or

. The discontinuity in the Holevo bound exactly at these extreme points was observed before and corresponds to a point where the rank of the state changes [ 147 , 148 , 149 , 150 , 151 , 152 ]. The small rotation that we are trying to estimate changes the states

, which are are rank 1 states and are not decohered to states which have rank 2 and are decohered.…”

Section: Resultsmentioning

confidence: 73%

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Conlon

Lam

Assad

2023

Entropy

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This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka–Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

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“…Similarly, if we want to estimate a rotation about the y -axis only any state with

will be optimal, except when

is exactly equal to 0 or

, which are are rank 1 states and are not decohered to states which have rank 2 and are decohered.…”

Section: Resultsmentioning

confidence: 73%

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Conlon

Lam

Assad

2023

Entropy

View full text Add to dashboard Cite

show abstract

“…( 5) when the support of the density matrix is modified by a variation of the parameter X , which may happen, e.g., when the state is pure. This point has been discussed in [70][71][72][73]. In the case of a pure state, we have:…”

Section: Definition 1 (Qfi)mentioning

confidence: 93%

Optimal control strategies for parameter estimation of quantum systems

Ansel,

Dionis,

Sugny

2024

SciPost Phys.

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Optimal control theory is an effective tool to improve parameter estimation of quantum systems. Different methods can be employed for the design of the control protocol. They can be based either on Quantum Fischer Information (QFI) maximization or selective control processes. We describe the similarities, differences, and advantages of these two approaches. A detailed comparative study is presented for estimating the parameters of a spin-1/2 system coupled to a bosonic bath. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible or when the experimental setup is not adapted to the QFI. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI.

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Fully‐Optimized Quantum Metrology: Framework, Tools, and Applications

Liu,

Hu,

Yuan

et al. 2024

Adv Quantum Tech

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This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The approach outputs the maximal attainable precision (in terms of the maximum of quantum Fisher information) as a semidefinite program and optimal strategies as feasible solutions thereof. Remarkably, the approach can identify the optimal precision for different sets of strategies, including parallel, sequential, quantum SWITCH‐enhanced, causally superposed, and generic indefinite‐causal‐order strategies. The tutorial consists of a pedagogic introduction to the background and mathematical tools of optimal quantum metrology, a detailed derivation of the main approach, and various concrete examples. As shown in the tutorial, applications of the approach include, but are not limited to, strict hierarchy of strategies in noisy quantum metrology, memory effect in non‐Markovian metrology, and designing optimal strategies. Compared with traditional approaches, the approach here yields the exact value of the optimal precision, offering more accurate criteria for experiments and practical applications. It also allows for the comparison between conventional strategies and the recently discovered causally‐indefinite strategies, serving as a powerful tool for exploring this new area of quantum metrology.

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Quantum Cramér-Rao bound for quantum statistical models with parameter-dependent rank

Cited by 4 publications

References 35 publications

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels

Optimal control strategies for parameter estimation of quantum systems

Fully‐Optimized Quantum Metrology: Framework, Tools, and Applications

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