Toy model for a relational formulation of quantum theory

International Journal of Theoretical Physics

Volumn 45, Issue 7, 2006, Pages 1229-1255

  Poulin, David ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Quantum gravity; Quantum information; Relational quantum theory

Indexed keywords

EID: 33746266669     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-006-9052-0     Document Type: Article

References (53)

1. Aharonov, Y. and Kaufherr, T. (1984). Quantum frames of reference. Physical Review D 30, 368.
2. Aharonov, Y. and Susskind, L. (1967). Charge superselecion rule. Physical Review 155(5), 1428.
3. Baiz, J. (1995). Spin networks in nonperturbative quantum gravity. In L. H. Kauffman, (ed.) The Interface of Knots and Physics, American Mathematical Society, Hattiesburg Mississippi, p. 167.
4. Baez, J. C. (1996). Spin network states in gauge theory. Advances in Mathematics 117, 253.
5. Baez, J. C. (2000). An introduction to spin foam models of quantum gravity and BF theory. Lecture Notes in Physics 543, 25.
6. Bartlett, S. D., Rudolph, T., and Spekkens, R. W. (2004). Decoherence-full subspaces and the cryptographic power of a private shared reference frame. Physical Review A 70, 32307.
7. Bartlett, S. D., Rudolph, T., and Spekkens, R. W. (2005). Dialogue concerning two views on quantum coherences: factist and fictionist. quant-ph/0507214.
8. Busch, P. and Singh, J. (1998). Luders theorem for unsharp quantum effects. Physics Letters A 249, 10-24.
9. Caves, C. M., Fuchs, C. A., and Schack, R. (2002). Quantum probabilities as bayesian probabilities. Physsical Review A 65, 022305.
10. DeWitt, B. S. (1967). Quantum theory of gravity I: the canonical theory. Physical Review 160, 1113.
11. Freidel, L. and Livine, E. R. (2003). Spin networks for noncompact groups. Journal of Mathematical Physics 44, 1322.
12. Fuchs, C. A. (2002). Quantum foundations in the light of quantum information. In A. Gonis, (ed.) 2001 NATO Advanced Research Workshop "Decoherence and its implications in quantum computation and information transfer" Mikonos, Greece.
13. Girelli, F. and Livine, E. R. (2005). Reconstructing quantum geometry from quantum information: spin networks as harmonic oscillators. Classical and Quantum Gravity 22, 3295.
14. Giovannetti, V., Lloyd, S., and Maccone, L. (2004). Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330.
15. Gambini, R. and Porto, R. A. (2001). Relational time in generally covariant quantum systems: four models. Physical Review D 63, 105014.
16. Gambini, R., Porto, R., and Pullin, J. (2004). A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for decoherence. New Journal of Physics 6, 45.
17. Gambini, R., Porto, R., and Pullin, J. (2005). Fundamental decoherence in quantum gravity. Brazilian Journal of Physics 35, 266.
18. Goldstone, J., Salam, A., and Weinberg, S. (1962). Broken symmetries. Physical Review 127, 965.
19. Haag, R. (1992). Local Quantum Physics: Fields, Particles, Algebras. Springer.
20. Hartle, J. B., Laflamme, R., and Marolf, D. (1995). Conservation laws in the quantum mechanics of closed systems. Physical Review D 51, 7007.
21. Kempe, J., Bacon, D., Lidar, D. A., and Whaley, K. B. (2001). Theory of decoherence-free fault-tolerant universal quantum compuation. Physical Review A 63, 42307.
22. Kershaw, D., and Woo, C. H. (1974). Experimental test for the charge superselection rule. Physical Review Letters 33(15).
23. Kribs, D., Laflamme, R., and Poulin, D. (2005). A unified and generalized approach to quantum error correction. Physical Review Letters 94, 180501.
24. Knill, E., Laflamme, R., and Viola, L. (2002). Theory of quantum error correction for general noise. Physical Review Letters 84, 2525-2528.
25. Kraus, K. (1983). States, Effects and Operations. Fundamental Notions of Quantum Theory, Academic Press, Berlin.
26. Kogut, J. B. and Susskind, L. (1975). Hamiltonian formulation of Wilson's lattice gauge theories. Physical Review D 11, 395.
27. Leggett, A. J. (2000). Topics in the theory of the ultracold dilute alkali gases. In C. M. Savage and M. -P. Das, (eds.), Bose-Einstein Condensation, p.1.
28. Lindblad, G. (1999). A general no-cloning theorem. Letter in Mathematical Physics 47, 189-196.
29. Lloyd, S. (2005). The computational universe: quantum gravity from quantum computation.
30. Major, S. (1999). A spin network primer. American Journal of Physics 67, 972.
31. Marolf, D. (2000). Group averaging and refined algebraic quantization: Where are we now?
32. Mazzucchi, S. (2000). On the observables describing a quantum reference frame. arxiv.org:quant-ph/0006060
33. Milburn, G. J. (2003). Lorentz invariant intrinsic decoherence.
34. Milburn, G. J. and Poulin, D. (2005). Relational time for systems of oscillators. International Journal of Quantum Info.
35. Mølmer, K. (1997). Optical coherence: a convenient fiction. Physical Review A 55, 3195.
36. Nielsen, M. A., and Poulin, D. (2005). Algebraic and information- theoretic conditions for operator quantum error-correction.
37. Ollivier, H., Poulin, D., and Zurek, W. H. (2004). Objective properties from subjective quantum states: environment as a witness. Physical Review Letters 93, 220401.
38. Pegg, D. T. (1991). Time in a quantum mechanical world. Journal of Physics 24, 3031.
39. Penrose, R. (1971). Angular momentum: an approach to combinatorial space-time. In T. Bastin, editor. Quantum Theory and Beyond, Cambridge University Press, Cambridge, UK. p. 151.
40. Poulin, D. (2004). Emergence of a classical world from within quantum theory. PhD thesis, University of Waterloo, Providence, RI (Rhode Island), USA.
41. Page, D. N. and Wootters, W. K. (1983). Evolution without evolution : dynamics described by stationary observables. Physical Review D 27, 2885.
42. Rovelli, C. (1991). Quantum reference systems. Classical and Quantum Gravity 8, 317.
43. Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics 35, 1637.
44. Rovelli, C. (2004). Quantum Gravity, Cambridge University Press, Cambridge, UK.
45. Rovelli, C. and Smolin, L. (1995). Spin networks and quantum gravity. Physical Review D 52, 5743.
46. Sakurai, J. (1994). Modern quantum mechanics, Addison-Welay,Ontario, Canada.
47. Toller, M. (1997). Quantum reference frames and quantum transformations. Il Nuovo Cimento 112, 1013.
48. Unruh, W. G. and Wald, R. M. (1989). Time and the interpretation of canon ical quantum gravity. Physical Review D 40, 2598.
49. von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press, New Jersey.
50. Wheeler, J. A. (1991). Information, physics, quantum: The search for links. In W. H. Zurek, (ed.) Complexity, Entropy and the Physics of Information, Addison-Wesley, Ontario, Canada.
51. Wigner, E. P. (1957). Relativistic invariance and quantum phenomena. Reviews of Modern Physics 29, 255.
52. Zanardi, P. (2001). Stabilizing quantum information. Physical Review A 63, 12301.
53. Zurek, W. H. (2003). Decoherence, einselection and the quantum origins of the classical. Reviews of Modern Physics 75, 715-775.