Optimal estimation of parameters for Schwinger effect
Tóm tắt
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.
Tài liệu tham khảo
Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439–3443 (1994)
Braunstein, S.L., Caves, C.M., Milburn, G.J.: Generalized uncertainty relations: theory, examples, and Lorentz invariance. Ann. Phys. (NY) 247, 135–173 (1996)
Petz, D.: Monotone metrics on matrix spaces. Linear Algebra Appl. 244, 81–96 (1996)
Petz, D., Ghinea, C.: Introduction to quantum Fisher information, QP-PQ: Quantum Probability and White Noise Analysis (World Scientific, Singapore, 2011), 27, 261–281
Giovanetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum Metrology. Phys. Rev. Lett. 96(1–4), 010401 (2006)
Huang, Z.M.: Protecting quantum Fisher information in curved space-time. Eur. Phys. J. Plus 133(1–8), 101 (2018)
Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic, New York (1976)
Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland Publishing Company, Amsterdam (1982)
Wang, J., Tian, Z., Jing, J., Fan, H.: Parameter estimation for an expanding universe. Nucl. Phys. B 892, 390–399 (2015)
Liu, X., Tian, Z., Wang, J., Jing, J.: Optimal estimation of parameters for scalar fields in expanding universe exhibiting Lorentz invariance violation, arXiv:1810.09120 (2018)
Vallisneri, M.: Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects. Phys. Rev. D 77(1–20), 042001 (2008)
Aasi, J., et al.: Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photonics 7, 613–619 (2013)
Aspachs, M., Adesso, G., Fuentes, I.: Optimal Quantum Estimation of the Unruh-Hawking Effect. Phys. Rev. Lett. 105(1–4), 151301 (2010)
Hosler, D., Kok, P.: Parameter estimation using NOON states over a relativistic quantum channel. Phys. Rev. A 88(1–5), 052112 (2013)
Yao, Y., Xiao, X., Ge, L., Wang, X.G., Sun, C.P.: Quantum Fisher information in noninertial frames. Phys. Rev. A 89(1–8), 042336 (2014)
Tian, Z., Wang, J., Jing, J., Fan, H.: Relativistic quantum metrology in open system dynamics. Sci. Rep. 5(1–6), 07946 (2015)
Genoni, M.G., Giorda, P., Paris, M.G.A.: Optimal estimation of entanglement. Phys. Rev. A 78(1–9), 032303 (2008)
Schwinger, J.: On Gauge invariance and vacuum polarization. Phys. Rev. 82, 664–679 (1951)
Di Piazza, A., Mller, C., Hatsagortsyan, K.Z., Keitel, C.H.: Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 1177–1228 (2012)
Gould, O., Mangles, S., Rajantie, A., Rose, S., Xie, C.: Observing thermal Schwinger pair production. Phys. Rev. A 99(1–8), 052120 (2019)
Li, Y., Mao, Q., Shi, Y.: Schwinger effect of a relativistic boson entangled with a qubit. Phys. Rev. A 99(1–8), 032340 (2019)
Li, Y., Dai, Y., Shi, Y.: Pairwise mode entanglement in Schwinger production of particle-antiparticle pairs in an electric field. Phys. Rev. D 95(1–13), 036006 (2017)
Ebadi, Z., Mirza, B.: Entanglement generation by electric field background. Ann. Phys. (NY, NY, US) 351, 363–381 (2014)
Kim, S.P., Lee, H.K., Yoon, Y.: Effective action of QED in electric field backgrounds. Phys. Rev. D 78(1–10), 105013 (2008)
Fisher, R.A.: Theory of statistical estimation. Proc. Camb. Philos. Soc. 22, 700–725 (1925)
Pairs, M.G.A.: Quantum estimation for quantum technology. Int. J. Quantum Inf. 7, 125–137 (2009)
Liu, J., Jing, X.X., Wang, X.G.: Phase-matching condition for enhancement of phase sensitivity in quantum metrology. Phys. Rev. A 88(1–4), 042316 (2013)
Zhang, Y.M., Li, X.W., Yang, W., Jin, G.R.: Quantum Fisher information of entangled coherent states in the presence of photon loss. Phys. Rev. A 88(1–7), 043832 (2013)
Yanovsky, V., Chvykov, V., Kalinchenko, G., Rousseau, P., Planchon, T., Matsuoka, T., Maksimchuk, A., Nees, J., Cheriaux, G., Mourou, G., Krushelnick, K.: Ultra-high intensity-300-TW laser at 0.1Hz repetition rate. Opt. Express 16, 2109–2114 (2008)
Monin, A., Voloshin, M.B.: Photon-stimulated production of electron-positron pairs in an electric field. Phys. Rev. D 81(1–6), 025001 (2010)
Bulanov, S.S., Mur, V.D., Narozhny, N.B., Nees, J., Popov, V.S.: Multiple colliding electromagnetic pulses: A way to lower the threshold of \(e^{+}e^{-}\) pair production from vacuum. Phys. Rev. Lett. 104(1–4), 220404 (2010)