Optimal estimation of parameters for Schwinger effect
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Optimal estimation of parameters for Schwinger effect Shu-Min Wu1
· Hao-Sheng Zeng1
Received: 3 September 2019 / Accepted: 28 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We study the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for excitations of Dirac field under a strong electric field. The study is carried out by employing the key concept of quantum metrology–quantum Fisher information. We find that the quality of estimation is very sensitive to characteristic parameters of the Dirac field. By suitably designing the characteristic parameters, such as the strength, momentum, mass, charge of the Dirac particles, high-precision estimation of parameters may be realized. Both the constant and pulsed electric field Schwinger effects are considered. Keywords Schwinger effect · Quantum Fisher information · Dirac particles
1 Introduction Recently, the topic of quantum Fisher information (QFI) [1–4] has received much attention in modern physics, not only due to its own significance in quantum information theory and quantum estimation theory, but also associated with rapid progress in quantum-enhanced metrology [5–7]. In fact, as the quantum measure of information of quantum states, the QFI play an important role in quantum statistical inference via its inextricable relationship with Cramér–Rao inequality [8,9]. Therefore, there will naturally be optimization problems, which can be appropriately solved in the framework of local quantum estimation theory (QET), providing an analytical tool to find the best measurement based on some given criteria. The application of QET-related example is as follows: optimal estimation of parameters in an expanding universe [10,11], enhanced sensitivity of gravitational wave detection [12,13], optimal quantum estima-
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Hao-Sheng Zeng [email protected] Shu-Min Wu [email protected]
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Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, and Department of Physics, Hunan Normal University, Changsha 410081, China 0123456789().: V,-vol
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S.-M. Wu, H.-S. Zeng
tion of the Unruh–Hawking effect [14–17], optimal estimation of entanglement [18] and so on. It is well known that a strong electromagnetic field can make the quantum vacuum become unstable and decay into pairs of charged particles [19]. This is known as the Schwinger production of electron–positron pairs or Schwinger effect. Although many experiments try hard to observe the Schwinger effect, no one has succeeded [20]. The reason is that the rate is too low. Recently, Gould et al. study the possibility of observing Schwinger pair production enhanced by a thermal bath of photons [21], and Li et al. use the concept of quantum entanglement and mutual information to analyze the Schwinger effect on an entangled state coupled with an electric field [22,23]. Ebadi et al. propose and demonstrate that this electric
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