Fundamental limit on "interaction-free" measurements

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 5, 2000, Pages 521031-521034

  Simon, Steven H ^a   Platzman, P M ^a  

^a LUCENT TECHNOLOGIES   (United States)

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EID: 0346481056     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

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2. P. Kwiat et al., Phys. Rev. Lett. 74, 4763 (1995).
3. A.G. White, J.R. Mitchell, O. Nairz, and P. Kwiat, Phys. Rev. A 58, 605 (1998).
4. T. Tsegaye et al., Phys. Rev. A 57, 3987 (1998).
5. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
6. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
7. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
8. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
9. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
10. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
11. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
12. Some other interesting discussions of interaction free measurements are C. Bennett, Nature (London) 371, 479 (1994); L. Hardy, Phys. Rev. Lett. 68, 2981 (1992); Phys. Lett. A 167, 11 (1992); L. Vaidman, Quantum Opt. 6, 119 (1994); H. Paul and M. Pavicic, J. Opt. Soc. Am. B 14, 1275 (1997); J.-S. Jang, Phys. Rev. A 59, 2322 (1999); G. Krenn, J. Summhammer, and K. Svozil, ibid. 53, 1228 (1996); M. Hafner and J. Summhammer, Phys. Lett. A 234, 563 (1997).
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16. A. Luis and L.L. Sánchez-Soto, Phys. Rev. A 58, 836 (1998); 60, 56 (1999).
17. See, for example, P. Kwiat et al., Sci. Am. (Int. Ed.) 275, 72 (1996); R. Penrose, Shadows of the Mind (Oxford University Press, Oxford, 1994).
18. See, for example, P. Kwiat et al., Sci. Am. (Int. Ed.) 275, 72 (1996); R. Penrose, Shadows of the Mind (Oxford University Press, Oxford, 1994).
19. E.H. du Marchi Van Voorthuysen, Am. J. Phys. 64, 1504 (1996).
20. Most generally, the prearranged region (the dotted box) might be of any given size. It is clear, however, that for the interferometric scheme of Ref. [1] to work, this prearranged region must be small enough such that the bomb will always block the beam line if placed within this region. In this case, we must have the region on the order of the size of the bomb in the transverse direction, and on the order of the length of the beam line in the longitudinal direction.
21. e is the probability of exploding the bomb [2]. It has been pointed out that, by using a multiple reflection geometry equivalent to a resonant cavity [2], one can make the experiment virtually 100% efficient - in the sense that we almost never blow up the bomb. For our current purposes, however, the simple interferometer will be a sufficient example, and the results will apply more generally.
22. J.D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).