Ancilla-assisted enhancement of channel estimation for low-noise parameters

Hotta, Masahiro; Karasawa, Tokishiro; Ozawa, Masanao

doi:10.1103/physreva.72.052334

Cited by 31 publications

(38 citation statements)

References 34 publications

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“…As pointed out in Ref. [2], in order to maximize the output Fisher information, it is sufficient to adopt an ancilla state space with dimensions equal to that of the object system. Therefore, we can assume that the ancilla state space is decomposed into N identical spaces.…”

Section: Introductionmentioning

confidence: 99%

“…We have introduced the notion of low-noise quantum channels Γ ǫ characterized by one low-noise parameter ǫ in an earlier paper [2]. Low-noise quantum channels are very useful for many physical applications, including relaxation processes driven by a thermal bath, decoherence of quantum computers, and rare processes in elementary particle physics.…”

Section: Introductionmentioning

confidence: 99%

“…In this section, we give a brief review of low-noise channels parametrized by the non-negative low-noise parameter ǫ [2]. The channels are defined in the Kraus representation as…”

mentioning

confidence: 99%

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

Hotta

Karasawa

Ozawa

2006

J. Phys. A: Math. Gen.

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The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005) ]. An estimation theory of low-noise parameters of channels has also been developed. In this report, we address the low-noise parameter estimation problem for the N -body extension of low-noise channels. We perturbatively calculate the Fisher information of the output states in order to evaluate the lower-bound of the mean-square error of the parameter estimation. We show that the maximum of the Fisher information over all input states can be attained by a factorized input state in the leading order of the low-noise parameter. Thus, to achieve optimal estimation, it is not necessary for there to be entanglement of the N subsystems, as long as the true low-noise parameter is sufficiently small.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hotta

Karasawa

Ozawa

2006

J. Phys. A: Math. Gen.

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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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“…Both quantities do not correspond to observables in a strict sense and therefore we have to resort to indirect measurements performed on the quantum probe to infer their value. In order to optimize this inference procedure we employ tools from local quantum esti-mation theory [19][20][21][22][23][24], which have already been proved useful in the estimation of static noise parameters [25][26][27][28][29] and in several other scenarios, as for example the estimation of quantum correlations [30][31][32][33], Gaussian states [34][35][36], optical phase [37][38][39][40][41][42], critical systems [43,44] and quantum thermometry [45]. In particular, we will optimize the initial preparation of the qubit and the interaction time in order to maximize the quantum Fisher information and the quantum signal-to-noise ratio.…”

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confidence: 99%

Quantum probes for the spectral properties of a classical environment

Benedetti

Buscemi

Bordone³

et al. 2014

Phys. Rev. A

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We address the use of simple quantum probes for the spectral characterization of classical noisy environments. In our scheme a qubit interacts with a classical stochastic field describing environmental noise and is then measured after a given interaction time in order to estimate the characteristic parameters of the noise. In particular, we address estimation of the spectral parameters of two relevant kinds of non-Gaussian noise: random telegraph noise with Lorentzian spectrum and colored noise with 1/f α spectrum. We analyze in details the estimation precision achievable by quantum probes and prove that population measurement on the qubit is optimal for noise estimation in both cases. We also evaluate the optimal interaction times for the quantum probe, i.e. the values maximizing the quantum Fisher information (QFI) and the quantum signal-to-noise ratio. For random telegraph noise the QFI is inversely proportional to the square of the switching rate, meaning that the quantum signal-to-noise ratio is constant and thus the switching rate may be uniformly estimated with the same precision in its whole range of variation. For colored noise, the precision achievable in the estimation of "color", i.e. of the exponent α, strongly depends on the structure of the environment, i.e. on the number of fluctuators describing the classical environment. For an environment modeled by a single random fluctuator estimation is more precise for pink noise, i.e. for α = 1, whereas by increasing the number of fluctuators, the quantum signal-to-noise ratio has two local maxima, with the largest one drifting towards α = 2, i.e. brown noise. In any communication channel or measurement scheme, the interaction of the information carriers with the external environment introduces noise in the system, thus degrading the overall performances. The precise characterization of the noise is thus a crucial ingredient for the design of highprecision measurements and reliable communication protocols. In many physical situations, the main source of noise is associated to the fluctuations of bistable quantities. In these cases, a suitable description of the noise is given in terms of classical stochastic processes [1][2][3]. In particular, in the case of phase damping, i.e. pure dephasing, it has been shown that the interaction of a quantum system with a quantum bath can be written in terms of a random unitary evolution driven by a classical stochastic process [4,5].The characterization of classical noise is often performed by collecting a series of measurements to estimate the autocorrelation function and the spectral properties [6][7][8][9][10][11]. This procedure is generally time consuming and may require the control of a complex system. A question thus arises on whether more effective techniques may be developed. To this purpose, we address the use of quantum probes to estimate the parameters of classical noise. We assume to have a quantum system interacting with the classical fluctuating field generating the noise and explore the performances of...

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Ancilla-assisted enhancement of channel estimation for low-noise parameters

Cited by 31 publications

References 34 publications

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

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

Quantum probes for fractional Gaussian processes

Quantum probes for the spectral properties of a classical environment

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