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Fitting magnetic field gradient with Heisenberg-scaling accuracy.

Zhang YL, Wang H, Jing L, Mu LZ, Fan H - Sci Rep (2014)

Bottom Line: Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB).We show that the estimated quantity achieves the Heisenberg-scaling accuracy.Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing 100871, China.

ABSTRACT
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

No MeSH data available.


Scheme of quantum parameter estimation.The finial state , evolved from a known initial state allowed by quantum mechanics, carries about the parameter vector characterizing dynamical process, and yest is obtained from the measurement results performed on the final state.
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f2: Scheme of quantum parameter estimation.The finial state , evolved from a known initial state allowed by quantum mechanics, carries about the parameter vector characterizing dynamical process, and yest is obtained from the measurement results performed on the final state.

Mentions: Then we take a random sample of size ν to estimate the parameter vector y via comparing the ratio of observed measurement outcomes with the probability distribution. An essential premise of effective deterministic estimation is requiring that the smooth map p(ξ/y) ↔ y is bijective. In order to avoid the periodical problems of determining the parameters yi, it is generally assumed that all components yi are small, which is called local estimation. For an effective deterministic observable random variable ξ, one estimates the parameter vector y via funtions based on experimental results. The general framework of quantum parameter estimation is shown in FIG. 2. Then the expectation and covariance matrix of estimation are


Fitting magnetic field gradient with Heisenberg-scaling accuracy.

Zhang YL, Wang H, Jing L, Mu LZ, Fan H - Sci Rep (2014)

Scheme of quantum parameter estimation.The finial state , evolved from a known initial state allowed by quantum mechanics, carries about the parameter vector characterizing dynamical process, and yest is obtained from the measurement results performed on the final state.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260217&req=5

f2: Scheme of quantum parameter estimation.The finial state , evolved from a known initial state allowed by quantum mechanics, carries about the parameter vector characterizing dynamical process, and yest is obtained from the measurement results performed on the final state.
Mentions: Then we take a random sample of size ν to estimate the parameter vector y via comparing the ratio of observed measurement outcomes with the probability distribution. An essential premise of effective deterministic estimation is requiring that the smooth map p(ξ/y) ↔ y is bijective. In order to avoid the periodical problems of determining the parameters yi, it is generally assumed that all components yi are small, which is called local estimation. For an effective deterministic observable random variable ξ, one estimates the parameter vector y via funtions based on experimental results. The general framework of quantum parameter estimation is shown in FIG. 2. Then the expectation and covariance matrix of estimation are

Bottom Line: Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB).We show that the estimated quantity achieves the Heisenberg-scaling accuracy.Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

View Article: PubMed Central - PubMed

Affiliation: School of Physics, Peking University, Beijing 100871, China.

ABSTRACT
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

No MeSH data available.