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13 - Entanglement, scaling, and the meaning of the wave function in protective measurement

from Part II - Meanings and implications

Published online by Cambridge University Press:  05 January 2015

By
Maximilian Schlosshauer  and
Tangereen V. B. Claringbold
Edited by
Shan Gao
Maximilian Schlosshauer
Affiliation:
University of Portland
Tangereen V. B. Claringbold
Affiliation:
University of Portland
Shan Gao
Affiliation:
Chinese Academy of Sciences
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Summary

We examine the entanglement and state disturbance arising in a protective measurement and argue that these inescapable effects doom the claim that protective measurement establishes the reality of the wave function. An additional challenge to this claim results from the exponential number of protective measurements required to reconstruct multi-qubit states. We suggest that the failure of protective measurement to settle the question of the meaning of the wave function is entirely expected, for protective measurement is but an application of the standard quantum formalism, and none of the hard foundational questions can ever be settled in this way.

Introduction

From the start, the technical result of protective measurement has been suggested to have implications for the interpretation of quantum mechanics. Consider how Aharonov and Vaidman [2] chose to begin their original paper introducing the idea of protective measurement:

We show that it is possible to measure the Schrödinger wave of a single quantum system. This provides a strong argument for associating physical reality with the quantum state of a single system.…

Since then, the pioneers of protective measurement seem to have taken a more moderate stance. Vaidman [42], in a recent synopsis of protective measurement, concedes that

the protective measurement procedure is not a proof that we should adopt one interpretation instead of the other, but it is a good testbed which shows advantages and disadvantages of various interpretations.

Notwithstanding this more subtle perspective and a number of critical studies of the technical and foundational aspects of protective measurement, Gao [21] has maintained, if not amplified, the force of Aharonov and Vaidman's original argument:

An immediate implication is that the result of a protective measurement, namely the expectation value of the measured observable in the measured state, reflects the actual physical property of the measured system, as the system is not disturbed after this result has been obtained.

[…]

Type
Chapter
Information
Protective Measurement and Quantum Reality
Towards a New Understanding of Quantum Mechanics
 , pp. 180 - 194
Publisher: Cambridge University Press
Print publication year: 2015

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References

[1] Aaronson, S. 2007. The learnability of quantum states. Proc. R. Soc. A, 463, 3089–3114.Google Scholar
[2] Aharonov, Y. and Vaidman, L. 1993. Measurement of the Schrödinger wave of a single particle. Phys. Lett. A, 178, 38–12.Google Scholar
[3] Aharonov, Y., Anandan, J., and Vaidman, L. 1993. Meaning of the wave function. Phys. Rev. A, 47, 4616–1626.Google Scholar
[4] Alter, O. and Yamamoto, Y. 1995. Inhibition of the measurement of the wave function of a single quantum system in repeated weak quantum nondemolition measurements. Phys. Rev. Lett., 74, 4106–4109.Google Scholar
[5] Alter, O. and Yamamoto, Y. 1996. Protective measurement of the wave function of a single squeezed harmonic oscillator state. Phys.Rev. A, 53, R2911–R2914.Google Scholar
[6] Alter, O. and Yamamoto, Y. 1997. Reply to “Comment on ‘Protective measurement of the wave function of a single squeezed harmonic oscillator state’”. Phys.Rev.A, 56, 1057–1059.Google Scholar
[7] Bell, J. S. 1964. On the Einstein–Podolsky–Rosen paradox. Physics, 1, 195–200.Google Scholar
[8] Bell, J. S. 1966. On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys., 38, 447–152.Google Scholar
[9] Camilleri, K. 2009. A history of entanglement: decoherence and the interpretation problem. Stud. Hist. Phil. Mod. Phys., 40, 290–302.Google Scholar
[10] Chen, J., Dawkins, H., Ji, Z., et al. 2013. Uniqueness of quantum states compatible with given measurement results. Phys. Rev. A, 88, 012109.Google Scholar
[11] Colbeck, R. and Renner, R. 2012. Is a system's wave function in one-to-one correspondence with its elements of reality?Phys. Rev. Lett., 108, 150402.Google Scholar
[12] D'Ariano, G. M. and Yuen, H. P. 1996. Impossibility of measuring the wave function of a single quantum system. Phys. Rev. Lett., 76, 2832–2835.Google Scholar
[13] Dass, N. D. H. and Qureshi, T. 1999. Critique of protective measurements. Phys. Rev. A, 59(4), 2590–2601.Google Scholar
[14] Dickson, M. 1995. An empirical reply to empiricism: protective measurement opens the door for quantum realism. Phil. Sci., 62, 122–140.Google Scholar
[15] Englert, B.-G. 2013. On quantum theory. Eur. Phys.J.D, 67, 238.Google Scholar
[16] Fuchs, C. A. and Schack, R. 2013. Quantum-Bayesian coherence. Rev. Mod. Phys., 85, 1693–1715.Google Scholar
[17] Fuchs, C. A. 2010. QBism, the perimeter of quantum Bayesianism. arXiv: 1003.5209v1 [quant-ph].
[18] Gao, S. 2011. Comment on “How to protect the interpretation of the wave function against protective measurements” by Jos Uffink. philsci-archive.pitt.edu/8942.
[19] Gao, S. 2013a. Distinct quantum states cannot be compatible with a single state of reality. philsci-archive.pitt.edu/9609.
[20] Gao, S. 2013b. On Uffink's criticism of protective measurements. Stud. Hist. Phil. Mod. Phys., 44, 513–518.Google Scholar
[21] Gao, S. 2013c. Protective measurement: a paradigm shift in understanding quantum mechanics. philsci-archive.pitt.edu/9627.
[22] Häffner, H., Hänsel, W., Roos, C. F., et al. 2005. Scalable multiparticle entanglement of trapped ions. Nature, 438, 643–646.Google Scholar
[23] Hardy, L. 2012. Are quantum states real? arXiv:1205.1439v3 [quant-ph].
[24] Heinosaari, T., Mazzarella, L., and Wolf, M. M. 2013. Quantum tomography under prior information. Comm. Math. Phys., 318, 355–374.Google Scholar
[25] İmamoğlu, A. 1993. Logical reversibility in quantum-nondemolition measurements. Phys.Rev.A, 47, R4577–R4580.Google Scholar
[26] Mermin, N. D. 2012. Quantum mechanics: fixing the shifty split. Phys. Today, 65, 8–10.Google Scholar
[27] Pusey, M. F., Barrett, J., and Rudolph, T. 2012. On the reality of the quantum state. Nature Phys., 8, 475–478.Google Scholar
[28] Rovelli, C. 1994. Comment on “Meaning of the wave function.”Phys. Rev. A, 50, 2788–2792.Google Scholar
[29] Samuel, J. and Nityananda, R. 1994. Comment on “Meaning of the wave function.” arXiv:gr-qc/9404051v1.
[30] Schlosshauer, M. 2004. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys., 76, 1267–1305.Google Scholar
[31] Schlosshauer, M. 2007. Decoherence and the Quantum-to-Classical Transition. 1st edn. Berlin/Heidelberg: Springer.
[32] Schlosshauer, M. 2011. Elegance and Enigma: the Quantum Interviews. 1st edn. Berlin/Heidelberg: Springer.
[33] Schlosshauer, M. and Fine, A. 2012. Implications of the Pusey–Barrett–Rudolph quantum no-go theorem. Phys. Rev. Lett, 108, 260404.Google Scholar
[34] Schlosshauer, M. and Fine, A. 2014. No-go theorem for the composition of quantum systems. Phys. Rev. Lett. 112, 070407Google Scholar
[35] Schwinger, J. 1993. Quantum mechanics: not mysterious. Science, 262, 826–827.Google Scholar
[36] Spekkens, R. W. 2007. Evidence for the epistemic view of quantum states: a toy theory. Phys. Rev. A, 75, 032110.Google Scholar
[37] Ueda, M. and Kitagawa, M. 1992. Reversibility in quantum measurement processes. Phys. Rev. Lett., 68, 3424–3427.Google Scholar
[38] Uffink, J. 1999. How to protect the interpretation of the wave function against protective measurements. Phys. Rev. A, 60, 3474–3481.Google Scholar
[39] Uffink, J. 2012. Reply to Gao's “Comment on ‘How to protect the interpretation of the wave function against protective measurements’ ”. philsci-archive.pitt.edu/9286.
[40] Uffink, J. 2013. Reply to Gao's “On Uffink's criticism of protective measurements.”Stud. Hist. Phil. Mod. Phys., 44, 519–523.Google Scholar
[41] Unruh, W. G. 1994. Reality and measurement of the wave function. Phys. Rev. A, 50, 882–887.Google Scholar
[42] Vaidman, L. 2009. Protective measurements. In: Greenberger, D., Hentschel, K., and Weinert, F. (eds.), Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy. Berlin/Heidelberg: Springer, pp. 505–508.Google Scholar
[43] Wallden, P. 2013. Distinguishing initial state-vectors from each other in histories formulations and the PBR argument. Found. Phys., 43, 1502–1525.Google Scholar
[44] Zeh, H. D. 1970. On the interpretation of measurement in quantum theory. Found. Phys., 1, 69–76.Google Scholar

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