Parameter Estimation of Quantum Channels

Ji, Zhengfeng; Wang, Guo‐Ming; Duan, Runyao; Feng, Yuan; Ying, Mingsheng

doi:10.1109/tit.2008.929940

Cited by 115 publications

(135 citation statements)

References 39 publications

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“…For this purpose it is useful to describe the correspondence x → ρ x in terms of a quantum channel Φ x which produces ρ x when acting on the initial input state ρ 0 of the probe, through the mapping Φ x (ρ 0 ) = ρ x . Aim of this section is to characterize the best estimate of x which can be obtained for a fixed number n of applications of Φ x , while optimizing with respect to the measurement, the estimation functions, and the choice of the initial state [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. This captures the basic aspects of most quantum metrology applications [5].…”

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

“…In the case of estimation of unitary channels, CQ has the same n −1/2 yield of CC, whereas QC and QQ can achieve the Heisenberg bound n −1 [24]. Non-unitary channels have equal or worse performances (since any non-unitary map can be purified into a unitary), depending on their action on the probes [24,25].…”

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

“…For the special case in which Φ x induces unitary transformations, this problem was analyzed in Refs. [25,26] where a scaling of order n −1 log n was achieved by means of local adaptive strategies. In Ref.…”

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

“…In Ref. [25] it was also observed that if the channels Φ x are programmable 5 then a sub-shot-noise scaling of the accuracy is not allowed. Examples for which the no-go theorem of [25] hold are provided by the class of classical channels (i.e.…”

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

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Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

Section: Quantum Parameter Estimation For Channelsmentioning

confidence: 99%

See 2 more Smart Citations

Advances in quantum metrology

2011

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“…In fact, quantum estimation theory has been successfully employed for the estimation of static noise parameters [43,44,45,46,47] and in several other scenarios, as for example quantum thermometry [48].…”

Section: The Physical Modelmentioning

confidence: 99%

Quantum probes for fractional Gaussian processes

Paris¹

2014

Physica A: Statistical Mechanics and its Applications

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We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional Brownian noise. We assume that the classical degree of freedom exposed to the environmental noise is coupled to a quantum degree of freedom of the same system, e.g. its spin, and exploit quantum limited measurements on the spin part to characterize the classical fractional noise. More generally, our approach may be applied to any two-level system subject to dephasing perturbations described by fractional Brownian noise, in order to assess the precision of quantum limited measurements in the characterization of the external noise. In order to assess the performances of quantum probes we evaluate the Bures metric, as well as the Helstrom and the Chernoff bound, and optimize their values over the interaction time. We find that quantum probes may be successfully employed to obtain a reliable characterization of fractional Gaussian process when the coupling with the environment is weak or strong. In the first case decoherence is not much detrimental and for long interaction times the probe acquires information about the environmental parameters without being too much mixed. Conversely, for strong coupling information is quickly impinged on the quantum probe and can effectively retrieved by measurements performed in the early stage of the evolution. In the intermediate situation, none of the two above effects take place: information is flowing from the environment to the probe too slowly compared to decoherence, and no measurements can be effectively employed to extract it from the quantum probe. The two regimes of weak and strong coupling are defined in terms of a threshold value of the coupling, which itself increases with the fractional dimension.

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Nonlocality Enhanced Precision in Quantum Polarimetry via Entangled Photons

Pedram,

Besaga,

Setzpfandt

et al. 2024

Adv Quantum Tech

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A nonlocal quantum approach is presented to polarimetry, leveraging the phenomenon of entanglement in photon pairs to enhance the precision in sample property determination. By employing two distinct channels, one containing the sample of interest and the other serving as a reference, the conditions are explored under which the inherent correlation between entangled photons can increase measurement sensitivity. Specifically, the quantum Fisher information (QFI) is calculated and compare the accuracy and sensitivity for the cases of single sample channel versus two channel quantum state tomography measurements. The theoretical results are verified by experimental analysis. The theoretical and experimental framework demonstrates that the nonlocal strategy enables enhanced precision and accuracy in extracting information about sample characteristics more than the local measurements. Depending on the chosen estimators and noise channels present, theoretical and experimental results show that noise‐induced bias decreases the precision for the estimated parameter. Such a quantum‐enhanced nonlocal polarimetry holds promise for advancing diverse fields including material science, biomedical imaging, and remote sensing, via high‐precision measurements through quantum entanglement.

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Parameter Estimation of Quantum Channels

Cited by 115 publications

References 39 publications

Advances in quantum metrology

Advances in quantum metrology

Quantum probes for fractional Gaussian processes

Nonlocality Enhanced Precision in Quantum Polarimetry via Entangled Photons

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