Entanglement and separability of quantum harmonic oscillator systems at finite temperature

Quantum Information and Computation

Volumn 8, Issue 3-4, 2008, Pages 245-262

  Anders, Janet ^a   Winter, Andreas ^a,b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Entanglement; Full separability; Harmonic chains; Thermal states

Indexed keywords

HARMONIC ANALYSIS; OSCILLATORS (MECHANICAL); QUANTUM ENTANGLEMENT; TEMPERATURE;

CRITICAL TEMPERATURES; ENTANGLEMENT; ENTANGLEMENT PROPERTIES; FINITE TEMPERATURES; FULL SEPARABILITY; HARMONIC CHAIN; OSCILLATOR SYSTEMS; QUANTUM HARMONIC OSCILLATORS; THERMAL; THERMAL STATE;

HAMILTONIANS;

EID: 45249116613     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: 10.26421/qic8.3-4-2     Document Type: Article

References (34)

1. A. Einstein. B. Podolsky and N. Rosen (1935), Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47:777.
2. E. Schrödinger (1935), Die gegenwärtige Situation in der Quantemmechanik, Naturwissenschaften 23:807-812, 823-828, 844-849;
3. Translated and reprinted in Quantum Theory and Measurement (1983), (J. A. Wheeler and W. H. Zurek, eds.), Princeton University Press, Princeton.
4. R. F. Werner (1989), Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,Phys. Rev. A 40:4277.
5. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters (1996), Mixed-state entanglement and quantum error correction,Phys. Rev. A 54(5):3824. (Pubitemid 126583604)
6. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters (1993), Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,Phys. Rev. Lett. 70(13):1895. (Pubitemid 23962871)
7. A. Ekert (1991), Quantum Cryptography Based on Bell's Theorem, Phys. Rev. Lett. 67:661.
8. M. Lewenstein, D. Brufi, J. I. Cirac, B. Kraus, M. Kus, J. Samsonowicz, A. Sanpera and R. Tarrach (2000), Separability and distillability in composite quantum systems - a primer,J. Mod. Optics 47(14-15):2481. (Pubitemid 35393024)
9. T. J. Osborne and M. A. Nielsen (2002), Entanglement, quantum phase transitions and density matrix renormalization, Quantum Inf. Proc. 1(1-2):45
10. T. J. Osborne and M. A. Nielsen (2002), Entanglement in a simple quantum phase transition, Phys. Rev. A 66(3):032110 (Pubitemid 35355546)
11. P. Zanardi and X. Wang (2002), Fermionic entanglement in itinerant systems, J. Phys. A: Math. Gen. 35:7947 (Pubitemid 37049262)
12. G. Vidal, J. I. Latorre, E. Rico and A. Kitaev (2003), Entanglement in Quantum Critical Phenomena, Phys. Rev. Lett. 90(2):227902.
13. L. Gurvits and H. N. Barnum (2003), Separable balls around the maximally mixed multipartite quantum states, Phys.Rev.A. 68:042312
14. Further results on the multipartite separable ball,quant-ph/0409095 (2004).
15. J. Anders, D. Kaszlikowski, C. Lunkes, T. Ohshima and V. Vedral (2006), Detecting entanglement with a thermometer, New J.P hys. 8:140. (Pubitemid 44273918)
16. J. Anders and V. Vedral (2007), Macroscopic Entanglement and Phase Transitions,OpenSyst. Inf. Dynamics 14:1.
17. L. Heaney, J. Anders and V. Vedral (2006), Spatial Entanglement ofa Free Bosonic Field,quant-ph/0607069v2.
18. P. Giorda and P. Zanardi (2004), Ground-state entanglement in interacting bosonic graphs,Euro-phys. Lett., 68(2):163. (Pubitemid 39453353)
19. S. L. Braunstein and A. K. Pati (eds.) (2003), Quantum Information with Continuous Variables, Kluwer, Dordrecht.
20. S. L. Braunstein and P. van Loock (2005), Quantum information with continuous variables,Rev. Mod. Phys. 77(2):513.
21. J. Anders, Thermal state entanglement in harmonic lattices, in preparation.
22. R. F. Werner and M. M. Wolf (2001), Bound Entangled Gaussian States, Phys. Rev. Lett. 86(16):3658.
23. J. Anders (2003), Estimating the Degree of Entanglement of Unknown Gaussian States, Diploma Thesis, Universitat Potsdam; quant-ph/0610263.
24. K. Audenaert, J. Eisert, M. B. Plenio and R. F. Werner (2002), Entanglement properties of the harmonic chain Phys. Rev. A 66:042327.
25. G. Giedke and J. I. Cirac (2002), The Characterisation of Gaussian Operations and Distillation ofGaussian States, Phys. Rev. A 66:032316. (Pubitemid 35355569)
26. M. M. Wolf, G. Giedke, O. Krüager, R. F. Werner and J. I, Cirac (2004), Gaussian Entanglement of Formation,Phys.Rev.A 69:052320
27. G. Giedke, M. M. Wolf, O. Kruager, R. F. Werner and J. I. Cirac (2003), Entanglement ofFormation for Symmetric Gaussian States, Phys. Rev. Lett. 1:107901.
28. J. Eisert, Ch. Simon and M. B. Plenio (2002), On the quantification of entanglement in infinite262 Entanglement and separability of quantum harmonic oscillator systems at finite temperature dimensional quantum systems, J. Phys. A: Math. Gen. 35 3911
29. M. Cramer, J. Eisert, M. B. Plenio and J. Dreissig (2006), Entanglement-area law for general bosonic harmonic lattice systems,Phys. Rev. A 73: 012309. (Pubitemid 43270058)
30. D. Cavalcanti, A. Ferraro, A. Garcia-Saez and A. Acin (2007), Thermal bound entanglement and area law, arXiv:0705.3762v1 [quant-ph].
31. S. J. van Enk (2003), Entanglement of electromagnetic fields,Phys. Rev. A 67:022303.
32. S. J. van Enk (2005), Single-particle entanglement,Phys. Rev. A 72:064306. (Pubitemid 43272676)
33. P. Zanardi (2001), Virtual Quantum Subsystems, Phy. Rev. Lett. 87:077901.
34. L. Heaney, J. Anders, D. Kaszlikowski and V. Vedral (2007), Spatial Entanglement From Off- Diagonal Long Range Order in a BEC,Phys. Rev.A76:053605