Skip to main content
×
×
Home
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Combes, Joshua Ferrie, Christopher Leifer, Matthew S. and Pusey, Matthew F. 2018. Why protective measurement does not establish the reality of the quantum state. Quantum Studies: Mathematics and Foundations, Vol. 5, Issue. 2, p. 189.

    Gao, Shan 2015. An argument for ψ-ontology in terms of protective measurements. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Vol. 52, Issue. , p. 198.

    ×
  • Print publication year: 2015
  • Online publication date: January 2015

10 - Protective measurement and the PBR theorem

from Part II - Meanings and implications
Summary

Protective measurements illustrate how Yakir Aharonov's fundamental insights into quantum theory yield new experimental paradigms that allow us to test quantum mechanics in ways that were not possible before. As for quantum theory itself, protective measurements demonstrate that a quantum state describes a single system, not only an ensemble of systems, and reveal a rich ontology in the quantum state of a single system. We discuss in what sense protective measurements anticipate the theorem of Pusey, Barrett, and Rudolph (PBR), stating that, if quantum predictions are correct, then two distinct quantum states cannot represent the same physical reality.

Introduction

Although protective measurements [1, 2] are a new tool for quantum theory and experiment, they have yet to find their way into the laboratory; also theorists have not put them to best use, beyond a 1993 paper by Anandan on “Protective measurement and quantum reality” [3]. In Section 10.2, we point out that protective measurements offer new experimental tests of quantum mechanics, and we review recent experiments attempting to measure quantum wave functions. In Section 10.3, we present the Pusey–Barrett–Rudolph (PBR) theorem and discuss their conclusion that the quantum state represents physical reality, and in Section 10.4, we discuss in what sense protective measurements anticipate this conclusion.

Protective measurement: implications for experiment and theory

In 1926, Schrödinger postulated his equation for “material waves” in analogy with light waves: paths of material particles – which obey the principle of least action – are an approximation to material waves, just as rays of light – which obey the principle of least time – are an approximation to light waves [4]. But Born soon discarded “the physical pictures of Schr00F6;dinger” [5] and gave the “material wave” Ψ(x, t) a new interpretation: |Ψ(x, t)|2 is the probability density to find a particle at x at time t. Even Schrödinger was obliged to accept Born's interpretation.

Recommend this book

Email your librarian or administrator to recommend adding this book to your organisation's collection.

Protective Measurement and Quantum Reality
  • Online ISBN: 9781107706927
  • Book DOI: https://doi.org/10.1017/CBO9781107706927
Please enter your name
Please enter a valid email address
Who would you like to send this to *
×
[1] Y., Aharonov and L., Vaidman, Measurement of the Schrödinger wave of a single particle, Phys. Lett. A178, 38 (1993).
[2] Y., Aharonov, J., Anandan and L., Vaidman, Meaning of the wave function, Phys. Rev. A47, 4616(1993).
[3] J., Anandan, Protective measurement and quantum reality, Found. Phys. Lett. 6 (1993).
[4] E., Schröidinger, Science, Theory and Man (London: Allen and Unwin), 1957, p. 177.
[5] M., Born, Zur Wellenmechanik der Stossvorgänge, Gött. Nachr. (1926), 146, cited and trans. in A., Pais, Niels Bohr's Times: in Physics, Philosophy and Polity (New York: Oxford University Press), 1991, p. 286.
[6] Y., Aharonov and D., Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Weinheim: Wiley-VCH), 2005, Chapter 15.
[7] J. S., Lundeen, B., Sutherland, A., Pater, C., Stewart and C., Bamber. Direct measurement of the quantum wavefunction, Nature 474, 188 (2011).
[8] J. S., Lundeen and C., Bamber, Procedure for direct measurement of general quantum states using weak measurement, Phys. Rev. Lett. 108, 070402 (2012).
[9] Y., Aharonov, D. Z., Albert and L., Vaidman, How the result of a measurement of a component of the spin of a spin-½ particle can turn out to be 100, Phys. Rev. Lett. 60, 1351 (1988); see also Y., Aharonov and D., Rohrlich, [6], Chapters 16–17.
[10] Y., Aharonov, private communication.
[11] A. S., Stodolna, A., Rouzée, F., Lépine et al., Hydrogen atoms under magnification: direct observation of the nodal structure of Stark states, Phys. Rev. Lett. 110, 213001 (2013).
[12] S., Cohen, M. M., Marb, A., Ollagnier et al., Wave function microscopy of quasibound atomic states, Phys. Rev. Lett. 110, 183001 (2013).
[13] D., Luftner, T., Ulesa, E. M., Reinisch et al., Imaging the wave function of adsorbed molecules, Proc. Nat. Acad. Sci. (USA), doi: 10.1073/pnas.1315716110 (2013).
[14] W., Heisenberg, Physics and Philosophy: the Revolution in Modern Science (New York: Harper and Row), 1958, p. 54.
[15] J. B., Hartle, Quantum mechanics of individual systems, Am.J.Phys. 36, 704 (1968).
[16] N., Harrigan and R. W., Spekkens, Einstein, incompleteness, and the espistemic view of quantum state, Found. Phys. 40, 125 (2010).
[17] A., Einstein, B., Podolsky and N., Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935), reprinted in Quantum Theory and Measurement, eds. J. A., Wheeler and W., Zurek (Princeton: Princeton University Press), 1983, pp. 138–141.
[18] N., Bohr, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 48, 696 (1935), reprinted in J. A., Wheeler and W., Zurek, (see [17]), pp. 145–151.
[19] M. F., Pusey, J., Barrett and T., Rudolph, On the reality of the quantum state, Nature Phys. 8, 475 (2012).
[20] J., Barrett, E. G., Cavalcanti, R., Lal and O.J. E., Maroney, No ψ-epistemic model can fully explain the indistinguishability of quantumm state, arXiv:1310.8302v1 (2013), Phys. Rev. Lett. 112, 250403 (2014).
[21] P. G., Lewis, D., Jennings, J., Barrett and T., Rudolph, Distinct quantum states can be compatible with a single state of reality, Phys. Rev. Lett. 109, 150404 (2012).
[22] J. S., Bell, Physics 1, 195 (1964).
[23] J. F., Clauser, M. A., Horne, A., Shimony and R. A., Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).
[24] L. E., Ballentine, The statistical interpretation of quantum mechanics, Rev. Mod. Phys. 42, 358 (1970).