True precision limits in quantum metrology

Jarzyna, Marcin; Demkowicz-Dobrzański, Rafał

doi:10.1088/1367-2630/17/1/013010

Cited by 89 publications

(88 citation statements)

References 48 publications

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“…Equations (9) and (12) are deemed as the decomposition of the Dirac fields in GHSdilation and Kruskal modes, respectively. Equations (9) and (12) are deemed as the decomposition of the Dirac fields in GHSdilation and Kruskal modes, respectively.…”

Section: Vacuum Structure Of Dirac Field In Ghs-dilation Black Hole Amentioning

confidence: 99%

“…where η ζ † k and l ζ k are the creation and annihilation operators applying to the Kruskal vacuum, respectively. Equations (9) and (12) are deemed as the decomposition of the Dirac fields in GHSdilation and Kruskal modes, respectively. Subsequently, it is easy to obtain some proper Bogoliubov transformations between the creation and annihilation operators in the GHS dilation and Kruskal coordinates.…”

Section: Vacuum Structure Of Dirac Field In Ghs-dilation Black Hole Amentioning

confidence: 99%

“…Later, Kraus first proposed a simplified formula, [5] which is given by H(X) + H(R) ≥ −log 2 c(X, R) ≡ q MU (2) and Maassen and Uffink provided a specific verification for this relation in 1988. [6] Basically, the EUR can be widely applied to a number of quantum tasks in the course of quantum information processing, that is, quantum random number generation, [7,8] quantum key distribution, [9][10][11] quantum metrology, [12] EPR steering, [13,14] quantum cryptography, [15,16] and entanglement witness. [17,18] Therefore, EUR has became a hot topic in the domain of quantum information science and many authors paid much attention on reforming the uncertainty relations in refs.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Measurement's Uncertainty in the Curved Space‐Time

2019

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The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle-Horowitz-Strominger dilation space-time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation-parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti-correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi-component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space-time.

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Section: Vacuum Structure Of Dirac Field In Ghs-dilation Black Hole Amentioning

confidence: 99%

Section: Vacuum Structure Of Dirac Field In Ghs-dilation Black Hole Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical Measurement's Uncertainty in the Curved Space‐Time

2019

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“…by incorporating the correlation C L are shown in (b) for projective measurements 0 h = and in (d) for weak measurements 0. h > As stressed above, the correlations among the acquired data are also available for the estimation in the sequential scheme. For instance, the two-point correlations C ℓ defined in (47) can be used to estimate .…”

Section: Sequential Schemementioning

confidence: 99%

Quantum estimation via sequential measurements

Burgarth

Giovannetti

et al. 2015

New J. Phys.

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The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a generalization of the central limit theorem in the present context, which under fairly general assumptions shows that as the number N of measurement data increases the probability distribution of functionals of the data (e.g., the average of the data) through which the target parameter is estimated becomes asymptotically normal and independent of the initial state of the probe. At variance with the previous studies (Guţă M 2011 Phys. Rev. A 83 062324; van Horssen M and Guţă M 2015 J. Math. Phys. 56 022109) we take a diagrammatic approach, which allows one to compute not only the leading orders in N of the moments of the average of the data but also those of the correlations among subsequent measurement outcomes. In particular our analysis points out that the latter, which are not available in usual i.i.d. data, can be exploited in order to improve the accuracy of the parameter estimation. An explicit application of our scheme is discussed by studying how the temperature of a thermal reservoir can be estimated via sequential measurements on a quantum probe in contact with the reservoir.See figure 1(a). In this context, the ultimate limits on the attainable precision in the estimation of g, optimized with respect to the general detection strategy, can be computed, resulting in the so-called quantum Cramér-Rao bound, which exhibits the functional dependence upon g r via the quantum Fisher information. See e.g. [2,3,[7][8][9][10][11][12].In many situations of physical interest, however, the possibility of reinitializing the setup to the same state is not necessarily guaranteed. In the present study we are going to consider a different scheme, in which a single probing system undergoes multiple applications of g L while being monitored during the process without being

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“…This makes the task of optimizing equation (13) a non-trivial matter. The most straightforward way to find the solution is to resort to numerical means [11,12,[30][31][32][33].…”

Section: Loss Transformationmentioning

confidence: 99%

Optimal lossy quantum interferometry in phase space

et al. 2017

Self Cite

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We analyse the phase space representation of the optimal measurement of a phase shift in an interferometer with equal photon loss in both its arms. In the local phase estimation scenario with a fixed number of photons, we identify features of the spin Wigner function that warrant sub-shotnoise precision, and discuss their sensitivity to losses. We derive the asymptotic form of an integral kernel describing the process of photon loss in the phase space in the limit of large photon numbers. The analytic form of this kernel allows one to assess the ultimate precision limit for a lossy interferometer. We also provide a general lower bound on the quantum Fisher information in terms of spin Wigner functions.

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True precision limits in quantum metrology

Cited by 89 publications

References 48 publications

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Dynamical Measurement's Uncertainty in the Curved Space‐Time

Quantum estimation via sequential measurements

Optimal lossy quantum interferometry in phase space

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