Macroscopic entanglement of many-magnon states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 3, 2005, Pages

  Morimae, Tomoyuki ^a,b   Sugita, Ayumu ^c   Shimizu, Akira ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c Osaka Prefecture University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

MACROSCOPIC ENTANGLEMENT; MANY-BODY STATES; MANY-MAGNON STATES; QUANTUM STATES;

ACOUSTIC NOISE; COMPUTATIONAL COMPLEXITY; ELECTRIC CHARGE; MAGNETIZATION; PHASE TRANSITIONS; QUANTUM THEORY; STATE ASSIGNMENT;

ATOMIC PHYSICS;

EID: 18544362478     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.032317     Document Type: Article

References (43)

1. A. Shimizu and T. Miyadera, Phys. Rev. Lett. 89, 270403 (2002).
2. A. Ukena and A. Shimizu, Phys. Rev. A 69, 022301 (2004).
3. A. Sugita and A. Shimizu, e-print quant-ph/0309217.
4. N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).
5. C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. A 63, 012307 (2000).
6. M. C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, 017901 (2001).
7. X. Wang, Phys. Rev. A 66, 044305 (2002).
8. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).
9. K. M. O'Connor and W. K. Wootters, Phys. Rev. A 63, 052302 (2001).
10. V. Subrahmanyam, Phys. Rev. A 69, 022311 (2004).
11. O. F. Syljuasen, Phys. Rev. A 68, 060301(R) (2003).
12. J. Vidal, G. Palacios, and R. Mosseri, Phys. Rev. A 69, 022107 (2004).
13. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. 92, 027901 (2004).
14. T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002).
15. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A 67, 022112 (2003).
16. D. Gunlycke, V. M. Kendon, V. Vedral, and S. Bose, Phys. Rev. A 64, 042302 (2001).
17. Y. Sun, Y. Chen, and H. Chen, Phys. Rev. A 68, 044301 (2003).
18. L. Zhou, H. S. Song, Y. Q. Guo, and C. Li, Phys. Rev. A 68, 024301 (2003).
19. G. L. Kamta and A. F. Starace, Phys. Rev. Lett. 88, 107901 (2002).
20. I. Bose and E. Chattopadhyay, Phys. Rev. A 66, 062320 (2002).
21. F. Verstraete, M. A. Martín-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004).
22. D. A. Meyer and R. Wallach, J. Math. Phys. 43, 4273 (2002).
23. N→∞f(N)/g(N)=0.
24. A. J. Leggett, Suppl. Prog. Theor. Phys. 69, 80 (1980).
25. A. J. Leggett, in Proceedings of the International Symposium on Foundations of Quantum Mechanics, Tokyo, 1983 (Physical Society of Japan, 1984), p. 74.
26. J. R. Friedman et al., Nature (London) 406, 43 (2000).
27. C. H. van der Wal et al., Science 290, 773 (2000).
28. I. Chiorescu et al., Science 299, 1869 (2003).
29. For example, a ten-atom molecule can be regarded as a single particle, ten particles, and many more particles (nuclei and electrons), in the energy ranges of ∼μeV, ∼meV, and ∼eV, respectively.
30. This statement would be understandable, from the discussion in endnote [31], for macroscopic variables that define equilibrium states. It is worth mentioning that the statement is also true for most macroscopic variables defining nonequilibrium states, such as the electric current density J. That is, the macroscopic current density J must be an average of the microscopic current density j over a macroscopic region. The spatial average introduces a smoothing effect, and J becomes a proper macroscopic variable.
31. Some of macroscopic variables, such as the volume and temperature, in thermodynamics cannot be represented as an additive operator. Although the volume is additive, it is usually considered as a boundary condition rather than a quantum-mechanical observable. We follow this convention. Regarding the temperature, it is a nonmechanical variable that can be defined only for equilibrium states. However, we note that at thermal equilibrium a macroscopic state is, hence the values of nonmechanical variables are, uniquely determined by a set of additive observables and the boundary conditions [L. Tisza, Ann. Phys. (N.Y.) 13, 1 (1961);
32. H. B. Callen, Thermodynamics (Wiley, New York, (1960)]. Therefore if two equilibrium states have distinct values of a nonmechanical variable they must have distinct values of some of the additive observables. It therefore seems that considering additive observables is sufficient.
33. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed., Pt. 1, (Butterworth-Heinemann, Oxford, 1980), Sec. XII.
34. The index p here is the same as p of Ref. [2], in which normalized additive operators were used instead of additive operators.
35. W. Marshall, Proc. R. Soc. London, Ser. A 232, 48 (1955).
36. P. Horsch and W. von der Linden, Z. Phys. B: Condens. Matter 72, 181 (1988).
37. T. Koma and H. Tasaki, J. Stat. Phys. 76, 745 (1994).
38. A. Shimizu and T. Miyadera, Phys. Rev. E 64, 056121 (2001).
39. A. Shimizu and T. Miyadera, J. Phys. Soc. Jpn. 71, 56 (2002).
40. Although other states are possible, they are beyond the scope of the present paper.
41. For spatially homogeneous states, p = 1 implies that the state has the cluster property. This is the case in the present paper because we only study translationally invariant states.
42. † is an approximate eigenstate of a Hamiltonian of a magnet Since an energy eigenstate is a stationary state, it is a state "after all possible propagation is finished." Therefore spatial propagation has already been incorporated into magnon states.
43. The generation of entanglement by the Hamilton dynamics was suggested in many works, e.g., Ref. [24].