Entanglement in relativistic quantum field theory

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 70, Issue 10, 2004, Pages

  Shi, Yu ^a,b  

^a TSINGHUA UNIVERSITY   (China)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ENERGY TRANSFER; MOLECULAR DYNAMICS; MOLECULAR INTERACTION; MOLECULAR RECOGNITION; PARTICLE SIZE; PHASE TRANSITION; QUANTUM MECHANICS;

EID: 19944418795     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.70.105001     Document Type: Article

References (38)

1. E. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935); E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951); J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
2. E. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935); E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951); J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
3. E. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935); E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951); J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
4. E. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935); E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935); D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951); J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
5. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).
6. E. Joos, H. D. Zeh, C. Kiefer, Claus Kiefer, D. Giulini, J. Kupsch, and I.-O Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory (Spriner-Verlag, Berlin, 2003); W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
7. E. Joos, H. D. Zeh, C. Kiefer, Claus Kiefer, D. Giulini, J. Kupsch, and I.-O Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory (Spriner-Verlag, Berlin, 2003); W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
8. H. D. Zeh, The Physical Basis of the Direction of time (Springer-Verlag, Berlin, 2001).
9. A. Peres, P. F. Scudo, and D. R. Terno, Phys. Rev. Lett. 88, 230402 (2002); P. M. Alsing and G. J. Milburn, quant-ph/0203051; R. M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002); For a review, see A. Peres and D. R. Terno, Rev. Mod. Phys. 76, 93 (2004).
10. A. Peres, P. F. Scudo, and D. R. Terno, Phys. Rev. Lett. 88, 230402 (2002); P. M. Alsing and G. J. Milburn, quant-ph/0203051; R. M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002); For a review, see A. Peres and D. R. Terno, Rev. Mod. Phys. 76, 93 (2004).
11. A. Peres, P. F. Scudo, and D. R. Terno, Phys. Rev. Lett. 88, 230402 (2002); P. M. Alsing and G. J. Milburn, quant-ph/0203051; R. M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002); For a review, see A. Peres and D. R. Terno, Rev. Mod. Phys. 76, 93 (2004).
12. R. Verch and R. Werner, quant-ph/0403089.
13. Y. Shi, J. Phys. A 37, 6807 (2004); Phys. Rev. A 69, 032318 (2004).
14. Y. Shi, J. Phys. A 37, 6807 (2004); Phys. Rev. A 69, 032318 (2004).
15. P. Zanardi, Phys. Rev. A 65, 042101 (2002).
16. Y. Shi, Phys. Rev. A 67, 024301 (2003); Phys. Lett. A 309, 254 (2003).
17. Y. Shi, Phys. Rev. A 67, 024301 (2003); Phys. Lett. A 309, 254 (2003).
18. S. J. van Enk, Phys. Rev. A 67, 022303 (2003).
19. C. Kiefer, in Ref. [3].
20. Here is used a parenthesis in the ket notation of a single particle state, to avoid confusion with the "-second-quantized" states, which are denoted as the usual ket's.
21. S. Weinberg, Quantum Theory of Fields (Cambridge University, Cambridge, England, 1995), Vol. I.
22. While the definition of a creation operator is based on a single particle state [13], some authors regard the former as more fundamental. H. D. Zeh [Phys. Lett. A 309, 329 (2003)].
23. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
24. S. J. Summers and R. Werner, J. Math. Phys. (N.Y.) 28, 2440 (1987); 28, 2448 (1987); B. Reznik, A. Retzker, and J. Silman, quant-ph/0310058.
25. S. J. Summers and R. Werner, J. Math. Phys. (N.Y.) 28, 2440 (1987); 28, 2448 (1987); B. Reznik, A. Retzker, and J. Silman, quant-ph/0310058.
26. P. Calabrese and J. Cardy, J. Stat. Phys. 06, 002 (2004).
27. T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi, Phys. Rev. D 50, 3987 (1994). It is interesting to see that the entanglement entropy was recognized here before the quantum informational interpretation in Ref. [15]; Earlier, it had been studied as 'geometric entropy' in, e.g., G. 't Hooft, Nucl. Phys. B256, 727 (1985); C. Callen and F. Wilczek, Phys. Lett. 33B, 55 (1994).
28. T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi, Phys. Rev. D 50, 3987 (1994). It is interesting to see that the entanglement entropy was recognized here before the quantum informational interpretation in Ref. [15]; Earlier, it had been studied as 'geometric entropy' in, e.g., G. 't Hooft, Nucl. Phys. B256, 727 (1985); C. Callen and F. Wilczek, Phys. Lett. 33B, 55 (1994).
29. T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi, Phys. Rev. D 50, 3987 (1994). It is interesting to see that the entanglement entropy was recognized here before the quantum informational interpretation in Ref. [15]; Earlier, it had been studied as 'geometric entropy' in, e.g., G. 't Hooft, Nucl. Phys. B256, 727 (1985); C. Callen and F. Wilczek, Phys. Lett. 33B, 55 (1994).
30. T. Padmanabhan, Gen. Relativ. Gravit. 34, 2029 (2002); 35, 2097 (2003); Mod. Phys. Lett. A 17, 1147 (2002); gr-qc/0311036.
31. T. Padmanabhan, Gen. Relativ. Gravit. 34, 2029 (2002); 35, 2097 (2003); Mod. Phys. Lett. A 17, 1147 (2002); gr-qc/0311036.
32. T. Padmanabhan, Gen. Relativ. Gravit. 34, 2029 (2002); 35, 2097 (2003); Mod. Phys. Lett. A 17, 1147 (2002); gr-qc/0311036.
33. It is also discussed in, e.g., T. Jacobson, "Introductory Notes on Black Hole Thermodynamics," (unpublished); Classical and Quantum Black Hole, edited by P. Fré, V. Gorini, G. Magli, and U. Moschella (IoP, Bristol, 1998); C. Kiefer, Classical Quantum Gravity 18, L151 (2001); V. Vedral, Central Eur. J. Phys. 1, 289 (2003).
34. It is also discussed in, e.g., T. Jacobson, "Introductory Notes on Black Hole Thermodynamics," (unpublished); Classical and Quantum Black Hole, edited by P. Fré, V. Gorini, G. Magli, and U. Moschella (IoP, Bristol, 1998); C. Kiefer, Classical Quantum Gravity 18, L151 (2001); V. Vedral, Central Eur. J. Phys. 1, 289 (2003).
35. It is also discussed in, e.g., T. Jacobson, "Introductory Notes on Black Hole Thermodynamics," (unpublished); Classical and Quantum Black Hole, edited by P. Fré, V. Gorini, G. Magli, and U. Moschella (IoP, Bristol, 1998); C. Kiefer, Classical Quantum Gravity 18, L151 (2001); V. Vedral, Central Eur. J. Phys. 1, 289 (2003).
36. It is also discussed in, e.g., T. Jacobson, "Introductory Notes on Black Hole Thermodynamics," (unpublished); Classical and Quantum Black Hole, edited by P. Fré, V. Gorini, G. Magli, and U. Moschella (IoP, Bristol, 1998); C. Kiefer, Classical Quantum Gravity 18, L151 (2001); V. Vedral, Central Eur. J. Phys. 1, 289 (2003).
37. W. G. Unruh, Phys. Rev. D 14, 870 (1976).
38. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).