Maximum Fisher information in mixed state quantum systems

Luati, Alessandra

doi:10.1214/009053604000000436

Cited by 31 publications

(30 citation statements)

References 7 publications

(16 reference statements)

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“…(16) are usually expressed in terms of the eigen decomposition of L ξ . A complete POVM {M x ,x ∈ X } with general significance known [4,5,10] to satisfy Eq. (16) is the von Neumann measurement made by the rank-one projectors on the eigenstates of L ξ .…”

Section: A Optimal Performance In Estimationmentioning

confidence: 99%

Optimized probing states for qubit phase estimation with general quantum noise

Chapeau‐Blondeau

2015

Phys. Rev. A

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We exploit the theory of quantum estimation to investigate quantum state estimation in the presence of noise. The quantum Fisher information is used to assess the estimation performance. For the qubit in Bloch representation, general expressions are derived for the quantum score and then for the quantum Fisher information. From this latter expression, it is proved that the Fisher information always increases with the purity of the measured qubit state. An arbitrary quantum noise affecting the qubit is taken into account for its impact on the Fisher information. The task is then specified to estimating the phase of a qubit in a rotation around an arbitrary axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate. The analysis enables determination of the optimal probing states best resistant to the noise, and proves that they always are pure states but need to be specifically matched to the noise. This optimization is worked out for several noise models important to the qubit. An adaptive scheme and a Bayesian approach are presented to handle phase-dependent solutions.

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Section: A Optimal Performance In Estimationmentioning

confidence: 99%

Optimized probing states for qubit phase estimation with general quantum noise

Chapeau‐Blondeau

2015

Phys. Rev. A

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“…Recall, that for a single parameter the bound by the classical Fisher information matrix could be saturated by an appropriately chosen POVM, (54). This is no longer the case for the the estimation of multiple parameters [14,15]. That is, the final lower bound in (57) can not be obtained.…”

Section: The χ 2 -Test and Its Connection To Quantum Parameter Esmentioning

confidence: 97%

Quantum chi-squared and goodness of fit testing

Temme

Verstraete

2015

Journal of Mathematical Physics

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Band structure and accumulation point in the spectrum of quantum collision operator in a onedimensional molecular chain J. Math. Phys. 52, 023302 (2011) A quantum mechanical hypothesis test is presented for the hypothesis that a certain setup produces a given quantum state. Although the classical and the quantum problems are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. A goodness of fit test for i.i.d quantum states is developed and a max-min characterization for the optimal measurement is introduced. We find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiencies, and determine the associated divergence rates. We discuss the relationship of the quantum goodness of fit test to the problem of estimating multiple parameters from a density matrix. These problems are found to be closely related and we show that the largest error of an optimal strategy, determined by the smallest eigenvalue of the Fisher information matrix, is given by the divergence rate of the goodness of fit test. C 2015 AIP Publishing LLC.

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“…For quantum systems with a bidimensional Hilbert space, as those we are investigating in this paper, the optimal measurement is a projective one [49,50]. Besides, using Eqs.…”

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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Maximum Fisher information in mixed state quantum systems

Cited by 31 publications

References 7 publications

Optimized probing states for qubit phase estimation with general quantum noise

Optimized probing states for qubit phase estimation with general quantum noise

Quantum chi-squared and goodness of fit testing

Quantum probes for fractional Gaussian processes

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