We analyze the average fidelity (say, F) and the fidelity deviation (say, D) in noisy-channel quantum teleportation. Here, F represents how well teleportation is performed on average and D quantifies whether the teleportation is performed impartially on the given inputs, that is, the condition of universality. Our analysis results prove that the achievable maximum average fidelity ensures zero fidelity deviation, that is, perfect universality. This structural trait of teleportation is distinct from those of other limited-fidelity probabilistic quantum operations, for instance, universal-NOT or quantum cloning. This feature is confirmed again based on a tighter relationship between F and D in the qubit case. We then consider another realistic noise model where F decreases and D increases due to imperfect control. To alleviate such deterioration, we propose a machine-learning-based algorithm. We demonstrate by means of numerical simulations that the proposed algorithm can stabilize the system. Notably, the recovery process consists solely of the maximization of F, which reduces the control time, thus leading to a faster cure cycle.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)
S. Popescu, Phys. Rev. Lett. 72, 797 (1994)
N. Gisin, Phys. Lett. A 210, 157 (1996)
J. Barrett, Phys. Rev. A 64, 042305 (2001)
D. Cavalcanti, A. Acín, N. Brunner, T. Vértesi, Phys. Rev. A 87, 042104 (2013)
H. Jeong, M.S. Kim, Phys. Rev. A 65, 042305 (2002)
T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro, S. Glancy, Phys. Rev. A 68, 042319 (2003)
J. Bang, S.-W. Lee, H. Jeong, J. Lee, Phys. Rev. A 86, 062317 (2012)
J. Bang, J. Ryu, D. Kaszlikowski, J. Phys. A Math. Theor. 51, 135302 (2018)
R. Jozsa, J. Mod. Opt. 41, 2315 (1994)
V. Bužek, M. Hillery, R.F. Werner, Phys. Rev. A 60, 2626 (1999)
V. Bužek, M. Hillery, R.F. Werner, J. Mod. Opt. 47, 211 (2000)
V. Bužek, M. Hillery, Phys. Rev. A 54, 1844 (1996)
S.L. Braunstein, G.M. D’Ariano, G.J. Milburn, M.F. Sacchi, Phys. Rev. Lett. 84, 3486 (2000)
W. Son, J. Lee, M.S. Kim, Y.-J. Park, Phys. Rev. A 64, 064304 (2001)
M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 60, 1888 (1999)
A.R.R. Carvalho, F. Mintert, A. Buchleitner, Phys. Rev. Lett. 93, 230501 (2004)
N. Burić, Phys. Rev. A 77, 012321 (2008)
R.F. Werner, Phys. Rev. A 40, 4277 (1989)
S. Albeverio, S.-M. Fei, W.-L. Yang, Phys. Rev. A 66, 012301 (2002)
R. Bhatia, C. Davis, Commun. Math. Phys. 215, 239 (2000)
F.T. Hioe, J.H. Eberly, Phys. Rev. Lett. 47, 838 (1981)
W. Son, J. Lee, M.S. Kim, J. Phys. A 37, 11897 (2004)
J. Bang, J. Lim, S. Yoo, M. S. Kim, J. Lee, arXiv:0803.2976 (2008)
M. Reck, A. Zeilinger, H.J. Bernstein, P. Bertani, Phys. Rev. Lett. 73, 58 (1994)
J. Kim, J. Lee, S. Lee, Phys. Rev. A. 61, 032312 (2000)
L. Viola, E. Knill, S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999)
N. Khaneja, R. Brockett, S.J. Glaser, Phys. Rev. A 63, 032308 (2001)
JB thanks to M. Wieśniak and T. Vértesi for discussions. WS and JB thank to the financial support of the National Research Foundation (NRF) of Korea Grants (no. 2019R1A2C2005504 and no. NRF-2019M3E4A1079666), funded by the MSIP (Ministry of Science, ICT and Future Planning), Korea government. JR acknowledges the National Research Foundation of Korea (NRF) Grants (no. NRF-2020M3E4A1079792). JB and KB was supported by KIAS Individual Grants (no. CG061003 and no. CG074701), respectively. JB and KB was supported by the NRF Grant funded by the Korea government (MSIT) (no. 2020M3E4A1079939).
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Wooyeong Song and Junghee Ryu contributed equally to this work.
About this article
Cite this article
Song, W., Ryu, J., Baek, K. et al. Average fidelity and fidelity deviation in noisy quantum teleportation. J. Korean Phys. Soc. (2021). https://doi.org/10.1007/s40042-021-00097-z
- Quantum teleportation
- Quantum machine learning