Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article

Effects of quantum error correction on entanglement sudden death

Published: 01 January 2014 Publication History

Abstract

We investigate the effects of error correction on non-local quantum coherence as a function of time, extending the study by Sainz and Björk [1]. We consider error correction of amplitude damping, pure phase damping and combinations of amplitude and phase damping as they affect both fidelity and quantum entanglement. Initial two-qubit entanglement is encoded in arbitrary real superpositions of both Φ-type and Ψ-type Bell states. Our main focus is on the possibility of delay or prevention of ESD (early stage decoherence, or entanglement sudden death). We obtain the onset times for ESD as a function of the state-superposition mixing angle. Error correction affects entanglement and fidelity differently, and we exhibit initial entangled states for which error correction increases fidelity but decreases entanglement, and vice versa.

References

[1]
I. Sainz and G. Björk, Phys. Rev. A 77, 052307 (2008), and Int. J. Quantum Inf. 7, S245-255 (2008).
[2]
J. Preskill, Quantum Information and Computation, see Caltech Lecture Notes, http://theory.caltech.edu/preskill/ph229/.
[3]
M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
[4]
T. Yu and J.H. Eberly, Phys. Rev. B 68, 165322 (2003).
[5]
A theoretical treatment of ESD in spontaneous emission is given in: T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004), and an experimental observation in a photonic context is reported in M.P. Almeida et al., Science 316, 579 (2007). See J.H. Eberly and T. Yu, Science 316, 555 (2007) for comments.
[6]
K. Zyczkowski, P. Horodecki, M. Horodecki, and R. Horodecki, Phys. Rev. A 65, 012101 (2001).
[7]
W. Son, M.S. Kim, J. Lee and D. Ahn, J. Mod. Opt. 49, 1739 (2002).
[8]
S. Daffer, K. Wodkiewicz, J. K. McIver, Phys. Rev. A 67, 062312 (2003).
[9]
L. Diosi, in Irreversible Quantum Dynamics, edited by F. Benatti, R. Floreanini (Springer, New York, 2003), pp. 157-163.
[10]
P. J. Dodd and J. J. Halliwell, Phys. Rev. A 69, 052105 (2004).
[11]
T. Yu and J. H. Eberly, Science 323, 598 (2009).
[12]
X.F. Qian and J.H. Eberly, Phys. Lett. A 376, 2913 (2012).
[13]
See, for example, P.W. Shor, Phys. Rev. A 52, R2493-R2496 (1995); A. M. Steane, Phys. Rev. Lett. 77, 793 (1996); C. H. Bennett, D.P. DiVincenzo, J.A. Smolin, and W.K. Wootters, Phys. Rev. A 54, 3824 (1996).
[14]
R. Wickert, N.K. Bernardes and P. v. Loock, arXiv: 1004.1931 (2010).
[15]
P. W. Shor, Phys. Rev. A 52, R2493-R2496 (1995).
[16]
D. Gottesman, Stabilizer Codes and Quantum Error Correction, PhD thesis, California Institute of Technology, Pasedena, CA, USA, 1997.
[17]
H. Carmichael, Statistical Methods in Quantum Optics: Master Equations and Fokker-Planck Equations (Springer, Germany, 2002), p. 6.
[18]
W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
[19]
R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, Phys. Rev. Lett. 77, 198 (1996).
[20]
T. Yu and J.H. Eberly, Opt. Commun. 264, 393 (2006).
[21]
T. Yu and J.H. Eberly, Opt. Commun. 283, 676 (2010).
[22]
D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Phys. Rev. A 56, 2567 (1997).
[23]
R. Chaves, L. Aolita and A. Acín, Phys. Rev. A 86, 020301(R) (2012).

Cited By

View all
  • (2018)Analytical evidence of ultrafast generation of spin-motion entanglementQuantum Information & Computation10.5555/3179543.317954817:5-6(456-468)Online publication date: 27-Dec-2018

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Quantum Information & Computation
Quantum Information & Computation  Volume 14, Issue 1-2
January 2014
180 pages

Publisher

Rinton Press, Incorporated

Paramus, NJ

Publication History

Published: 01 January 2014
Revised: 09 April 2013
Received: 25 October 2012

Author Tags

  1. amplitude damping
  2. entanglement sudden death
  3. fidelity
  4. phase damping
  5. quantum error correction
  6. qubit entanglement

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 14 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2018)Analytical evidence of ultrafast generation of spin-motion entanglementQuantum Information & Computation10.5555/3179543.317954817:5-6(456-468)Online publication date: 27-Dec-2018

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media