Uncertainty relations for noise and disturbance in generalized quantum measurements

Annals of Physics

Volumn 311, Issue 2, 2004, Pages 350-416

  Ozawa, Masanao ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Completely positive maps; Disturbance; Generalized quantum measurement; Heisenberg: Uncertainty relation; Instruments; Measurements; Noise; Positive operator valued measures; Quantum nondemolition measurements; Uncertainty principle

Indexed keywords

EID: 2442681328     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aop.2003.12.012     Document Type: Article

References (62)

1. W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Z. Phys. 43 (1927) 172-198.
2. M. Ozawa, Physical content of Heisenberg's uncertainty relation: limitation and reformulation, Phys. Lett. A 318 (2003) 21-29.
3. E.H. Kennard, Zur Quantenmechanik einfacher Bewegungstypen, Z. Phys. 44 (1927) 326-352.
4. H.P. Robertson, The uncertainty principle, Phys. Rev. 34 (1929) 163-164.
5. W. Heisenberg, The Physical Principles of the Quantum Theory, University of Chicago Press, Chicago, 1930 [Reprinted by Dover, New York (1949, 1967)].
6. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932.
7. N. Bohr, Discussion with Einstein on epistemological problems in atomic physics, in: P.A. Shilpp (Ed.), Albert Einstein: Philosopher-Scientist, The Library of Living Philosophers, Evanston, 1949, pp. 200-241.
8. D. Bohm, Quantum Theory, Prentice-Hall, New York, 1951.
9. A. Messiah, Mécanique Quantique, vol. I, Dunod, Paris, 1959 [Quantum Mechanics, vol. I (North-Holland, Amsterdam, 1959)].
10. V.B. Braginsky, Y.I. Vorontsov, Quantum-mechanical limitations in macroscopic experiments and contemporary experimental technique, Uspehi Fiz. Nauk 114 (1974) 41-53.
11. V.B. Braginsky, Y.I. Vorontsov, Sov. Phys. Usp. 17 (1975) 644.
12. C.M. Caves, K.S. Thorne, R.W.P. Drever, V.D. Sandberg, M. Zimmermann, On the measurement of a weak classical force coupled with a quantum mechanical oscillator, I. Issues of principle, Rev. Mod. Phys. 52 (1980) 341.
13. V.B. Braginsky, Y.I. Vorontsov, K.S. Thorne, Quantum nondemolition measurements, Science 209 (1980) 547-557.
14. A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47 (1935) 777-780.
15. E. Arthurs, J.L. Kelly Jr., On the simultaneous measurement of a pair of conjugate observables, Bell. Syst. Tech. J. 44 (1965) 725-729.
16. L.E. Ballentine, The statistical interpretation of quantum mechanics, Rev. Mod. Phys. 42 (1970) 358-381.
17. H.P. Yuen, Contractive states and the standard quantum limit for monitoring free-mass positions, Phys. Rev. Lett. 51 (1983) 719-722.
18. K. Kraus, Complementary observables and uncertainty relations, Phys. Rev. D 35 (1987) 3070-3075.
19. E. Arthurs, M.S. Goodman, Quantum correlations: a generalized Heisenberg uncertainty relation, Phys. Rev. Lett. 60 (1988) 2447-2449.
20. M. Ozawa, Measurement breaking the standard quantum limit for free-mass position, Phys. Rev. Lett. 60 (1988) 385-388.
21. M. Ozawa, Realization of measurement and the standard quantum limit, in: P. Tombesi, E.R. Pike (Eds.), Squeezed and Nonclassical Light, Plenum, New York, 1989, pp. 263-286.
22. J. Hilgevoord, J. Uffink, A new view on the uncertainty principle, in: A.I. Miller (Ed.), Sixty-Two Years of Uncertainty, Plenum, New York, 1990, pp. 121-137.
23. H. Martens, W.M. de Muynck, The inaccuracy principle, Found. Phys. 20 (1990) 357-380.
24. M. Ozawa, Quantum limits of measurements and uncertainty principle, in: C. Bendjaballah, O. Hirota, S. Reynaud (Eds.), Quantum Aspects of Optical Communications, Springer, Berlin, 1991, pp. 3-17.
25. S. Ishikawa, Uncertainty relations in simultaneous measurements for arbitrary observables, Rep. Math. Phys. 29 (1991) 257-273.
26. H. Martens, W.M. de Muynck, Disturbance, conservation laws and the uncertainty principle, J. Phys. A 25 (1992) 4887-4901.
27. V.B. Braginsky, F.Y. Khalili, Quantum Measurement, Cambridge University Press, Cambridge, 1992.
28. D.M. Appleby, Int. J. Theor. Phys. 37 (1998) 1491.
29. M. Ozawa, Controlling quantum state reduction, Phys. Lett. A 282 (2001) 336-342.
30. M. Ozawa, Position measuring interactions and the Heisenberg uncertainty principle, Phys. Lett. A 299 (2002) 1-7.
31. E.B. Davies, J.T. Lewis, An operational approach to quantum probability, Commun. Math. Phys. 17 (1970) 239-260.
32. H.P. Yuen, Characterization and realization of general quantum measurements, in: M. Namiki et al. (Ed.), Proceedings of the Second International Symposium on Foundations of Quantum Mechanics, Physical Society of Japan, Tokyo, 1987, pp. 360-363.
33. M. Ozawa, Conditional expectation and repeated measurement of continuous quantum observables, in: Probability Theory and Mathematical Statistics, in: K. Itô, J.V. Prohorov (Eds.), Lecture Notes in Math., vol. 1021, Springer, Berlin, 1983, pp. 518-525.
34. M. Ozawa, Quantum measuring processes of continuous observables, J. Math. Phys. 25 (1984) 79-87.
35. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
36. M. Ozawa, Universally valid reformulation of the heisenberg uncertainty principle on noise and disturbance in measurement, Phys. Rev. A 67 (2003) 042105 (1-6).
37. P.A.M. Dirac, The Principles of Quantum Mechanics, fourth ed., Oxford University Press, Oxford, 1958.
38. A.N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitrechnung, Springer, Berlin, 1933 [Foundations of the Theory of Probability, Second English Edition, (Chelsea, New York, 1950)].
39. S.K. Berberian, Notes on Spectral Theory, Van Nostrand, Princeton, NJ, 1966.
40. M. Ozawa, Optimal measurements for general quantum systems, Rep. Math. Phys. 18 (1980) 11-28.
41. K. Kraus, States, Effects, and Operations: Fundamental Notions of Quantum Theory, Lecture Notes in Physics, vol. 190, Springer, Berlin, 1983.
42. C.W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York, 1976.
43. E.B. Davies, Quantum Theory of Open Systems, Academic Press, London, 1976.
44. A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam, 1982.
45. A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, Dordrecht, 1993.
46. P.R. Halmos, Introduction to Hilbert Space Theory and the Theory of Spectral Multiplicity, Chelsea, New York, 1951.
47. M. Ozawa, Quantum state reduction and the repeatability hypothesis, Ann. Jpn. Ass. Philos. Sci. 11 (2003) 107-121.
48. M. Ozawa, Measurements of nondegenerate discrete observables, Phys. Rev. A 62 (2000) 062101 (1-13).
49. M. Ozawa, Quantum measurement, information, and completely positive maps, in: P. Tombesi, O. Hirota (Eds.), Quantum Communication, Computing, and Measurement 3, Kluwer/Plenum, New York, 2001, pp. 97-106.
50. M. Ozawa, An operational approach to quantum state reduction, Ann. Phys. (N.Y.) 259 (1997) 121-137.
51. M. Ozawa, Conditional probability and a posteriori states in quantum mechanics, Publ. Res. Inst. Math. Sci., Kyoto Univ. 21 (1985) 279-295.
52. W.F. Stinespring, Positive functions on Calgebras, Proc. Am. Math. Soc. 6 (1955) 211-216.
53. K. Kraus, General state changes in quantum theory, Ann. Phys. (N.Y.) 64 (1971) 311-335.
54. M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
55. M. Ozawa, Operations, disturbance, and simultaneous measurability, Phys. Rev. A 63 (2001) 032109 (1-15).
56. M. Ozawa, Canonical approximate quantum measurements, J. Math. Phys. 34 (1993) 5596-5624.
57. F. Riesz, B.Sz. Nagy, Functional Analysis, Frederick Ungar, New York, 1955.
58. C.M. Caves, Defense of the standard quantum limit for free-mass position, Phys. Rev. Lett. 54 (1985) 2465-2468.
59. M. Ozawa, Quantum mechanical models of position measurements, Phys. Rev. A 41 (1990) 1735-1737.
60. G. Lüders, Über die Zustandsänderung durch den Messprozess, Ann. Phys. (Leipzig) 8 (6) (1951) 322-328.
61. M.D. Srinivas, Collapse postulate for observables with continuous spectra, Commun. Math. Phys. 71 (1980) 131-158.
62. M. Ozawa, Measuring processes and repeatability hypothesis, in: Probability Theory and Mathematical Statistics, in: S. Watanabe, Y. V. Prohorov (Eds.), Lecture Notes in Math., vol. 1299, Springer, Berlin, 1988, pp. 412-421.