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2 - Protective measurement of the wave function of a single system

from Part I - Fundamentals and applications

Published online by Cambridge University Press:  05 January 2015

By
Lev Vaidman
Edited by
Shan Gao
Lev Vaidman
Affiliation:
Tel Aviv University
Shan Gao
Affiliation:
Chinese Academy of Sciences
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Summary

My view on the meaning of the quantum wave function and its connection to protective measurements is described. The wave function and only the wave function is the ontology of the quantum theory. Protective measurements support this view although they do not provide a decisive proof. A brief review of the discovery and the criticism of protective measurement is presented. Protective measurements with postselection are discussed.

Introduction

In the first graduate course of quantum mechanics I remember asking the question: “Can we consider the wave function as a description of a single quantum system?” I got no answer. Twelve years later, in South Carolina, after I completed my Ph.D. studies at Tel Aviv University under the supervision of Yakir Aharonov in which we developed the theory of weak measurements [1], I asked Aharonov: Can we use weak measurement to observe the wave function of a single particle?

At that time I had already become a strong believer in the many-worlds interpretation (MWI) of quantum mechanics [2] and had no doubt that a single system is described by the wave function. Yakir Aharonov never shared with me the belief in the MWI. When we realized that using what is called now protective measurement, we can, under certain conditions, observe the wave function of a single quantum system, he was really excited by the result. At 1992 I was invited to a conference on the Foundations of Quantum Mechanics in Japan where I presented this result: “The Schrödinger wave is observable after all!”[3]. Then I went home to Tel Aviv where I finished writing a letter which received mixed reviews in Phys. Rev. Lett., while Jeeva Anandan, working on the topic with Aharonov in South Carolina, wrote a paper accepted in Phys. Rev. A [4]. After acceptance of the PRA paper it was hard to fight the referees in PRL, but PLA accepted it immediately [5].

Type
Chapter
Information
Protective Measurement and Quantum Reality
Towards a New Understanding of Quantum Mechanics
 , pp. 15 - 27
Publisher: Cambridge University Press
Print publication year: 2015

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References

[1] Y., Aharonov and L., Vaidman, Properties of a quantum system during the time interval between two measurements, Phys. Rev. A 41, 11 (1990).Google Scholar
[2] L., Vaidman, Many-worlds interpretation of quantum mechanics, Stan. Enc. Phil., E. N., Zalta (ed.) (2002), plato.stanford.edu/entries/qm-manyworlds/.Google Scholar
[3] Y., Aharonov and L., Vaidman, The Schrödinger wave is observable after all! In Quantum Control and Measurement, H., Ezawa and Y., Murayama (eds.), 99 (Tokyo: Elsevier Publishing, 1993).
[4] Y., Aharonov, J., Anandan, and L., Vaidman, Meaning of the wave function, Phys. Rev. A 47, 4616 (1993).Google Scholar
[5] Y., Aharonov and L., Vaidman, Measurement of the Schrodinger wave of a single particle, Phys. Lett. A 178, 38 (1993).Google Scholar
[6] M. F., Pusey, J., Barrett, and T., Rudolph, On the reality of the quantum state, Nature Phys. 8, 476 (2012).Google Scholar
[7] J. S., Lundeen, B., Sutherland, A., Patel, C., Stewart, and C., Bamber, Direct measurement of the quantum wavefunction, Nature 474, 188 (2011).Google Scholar
[8] R., Colbeck and R., Renner, Is a system's wave function in one-to-one correspondence with its elements of reality?Phys. Rev. Lett. 108, 150402 (2012).Google Scholar
[9] L., Hardy, Are quantum states real?Int. J. Mod. Phys. B, 27, 1345012 (2013).Google Scholar
[10] J. S., Bell, Beables for quantum field theory, in J. S., Bell, Speakable and Unspeak-able in Quantum Mechanics, pp. 173–180 (Cambridge: Cambridge University Press, 1987).
[11] B. G., Englert, M. O., Scully, G., Süssmann, and H., Walther, Surrealistic Bohm trajectories, Z. Naturforsch. A 47, 1175 (1992).Google Scholar
[12] Y., Aharonov and L., Vaidman, About position measurements which do not show the Bohmian particle position, in Bohmian Mechanics and Quantum Theory: an Appraisal, J. T., Cushing, A., Fine and S., Goldstein (eds.), pp. 141–154 (Dordrecht: Kluwer, 1996).
[13] Y., Aharonov, M. O., Scully, and B. G., Englert, Protective measurements and Bohm trajectories, Phys. Lett. A 263, 137 (1999).Google Scholar
[14] K., Gottfried, Does quantum mechanics describe the “collapse” of the wave function?, contribution to the Erice school: 62 Years of Uncertainty (unpublished) (1989).Google Scholar
[15] C. M., Caves, C. A., Fuchs, and R., Schack, Quantum probabilities as Bayesian probabilities, Phys. Rev. A 65, 022305 (2002).Google Scholar
[16] M. V., Berry, Five momenta, Eur. J. Phys. 34, 1337 (2013).Google Scholar
[17] Y., Aharonov, D. Z., Albert, and L., Vaidman, Measurement process in relativistic quantum theory, Phys. Rev. D 34, 1805 (1986).Google Scholar
[18] S., Popescu and L., Vaidman, Causality constraints on nonlocal quantum measurements, Phys. Rev. A 49, 4331 (1994).Google Scholar
[19] L., Vaidman, Nonlocality of a single photon revisited again, Phys. Rev. Lett. 75, 2063 (1995).Google Scholar
[20] Y., Aharonov and L., Vaidman, Nonlocal aspects of a quantum wave, Phys. Rev. A 61, 052108 (2000).Google Scholar
[21] K. J., Resch and A. M., Steinberg, Extracting joint weak values with local, single-particle measurements, Phys. Rev. Lett. 92, 130402 (2004).Google Scholar
[22] A., Broduch and L., Vaidman, Measurements of non local weak values, J. Phys.: Conf. Ser. 174, 012004 (2009).Google Scholar
[23] S., Cohen, M. M., Harb, A., Ollagnier, et al., Wave function microscopy of quasibound atomic states, Phys. Rev. Lett. 110, 183001 (2013).Google Scholar
[24] S., Nussinov, Scattering experiments for measuring the wave function of a single system, Phys. Lett. B 413, 382 (1997).Google Scholar
[25] Y., Aharonov and L., Vaidman, Complete description of a quantum system at a given time, J. Phys. A: Math. Gen. 24, 2315 (1991).Google Scholar
[26] L., Vaidman, Time symmetry and the many-worlds interpretation, in Many Worlds? Everett, Quantum Theory, and Reality, S., Saunders, J., Barrett, A., Kent, and D., Wallace (eds.) (Oxford: Oxford University Press, 2010).
[27] Y., Aharonov, and L., Vaidman, Protective measurements of two-state vectors, in Potentiality, Entanglement and Passion-at-a-Distance, R. S., Cohen, M., Horne and J., Stachel (eds.), BSPS 1-8, (Dordrecht: Kluwer, 1997).
[28] L., Vaidman, Weak-measurement elements of reality, Found. Phys. 26, 895 (1996).Google Scholar
[29] G. S., Paraoanu, Extraction of information from a single quantum, Phys. Rev. A 83, 044101 (2011).Google Scholar
[30] O., Alter and Y., Yamamoto, Protective measurement of the wave function of a single squeezed harmonic-oscillator state, Phys. Rev. A 53, R2911 (1996); Phys, Rev. A 56, 1057 (1997).Google Scholar
[31] Y., Aharonov and L., Vaidman, Protective measurement of the wave function of a single squeezed harmonic-oscillator state – comment, Phys.Rev.A 56, 1055 (1997).Google Scholar
[32] G. M., D'Ariano and H. P., Yuen, Impossibility of measuring the wave function of a single quantum system, Phys. Rev. Lett. 76, 2832 (1996).Google Scholar
[33] J., Uffink, How to protect the interpretation of the wave function against protective measurements, Phys. Rev. A 60, 3474 (1999).Google Scholar
[34] S., Gao, On Uffink's criticism of protective measurements, Stud. Hist. Phil. Mod. Phys. 44, 513 (2013).Google Scholar
[35] J., Uffink, Reply to Gao's “On Uffink's criticism of protective measurements”Stud. Hist. Phil. Mod. Phys. 44, 519 (2013).Google Scholar
[36] W. G., Unruh, Reality and measurement of the wave function, Phys.Rev.A 50, 882 (1994).Google Scholar
[37] P., Ghose and D., Home, An analysis of the Aharonov–Anandan–Vaidman model, Found. Phys. 25, 1105 (1995).Google Scholar
[38] M., Dickson, An empirical reply to empiricism: protective measurement opens the door for quantum realism, Phil. Sci. 62, 122 (1995).Google Scholar
[39] C., Rovelli, Meaning of the wave function – comment, Phys.Rev. A 50, 2788 (1994).Google Scholar
[40] Y., Aharonov, J., Anandan, and L., Vaidman, The meaning of protective measurements, Found. Phys. 26, 117 (1996).Google Scholar
[41] N. D. H., Dass and T., Qureshi, Critique of protective measurements, Phys.Rev. A 59, 2590 (1999).Google Scholar

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