Skip to main content
Log in

Illusory Decoherence

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Suppose a quantum experiment includes one or more random processes. Then the results of repeated measurements may appear consistent with irreversible decoherence even if the system’s evolution prior to measurement is reversible and unitary. Two thought experiments are constructed as examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. The quantum Loschmidt paradox should not be confused with the cosmological time-reversal paradox, which may or may not be related. See e.g. [2] for a discussion of both.

  2. To avoid the difficulty of flipping thousands of coins without attracting the suspicion of her advisor, suppose she automates this process with a quantum RNG instead of a coin.

  3. Similar experiments with different interferometer configurations have been performed with C60 “buckyballs” and even larger molecules [5, 6].

  4. The notation \(\hat{H}\) is chosen to suggest “heads,” not “Hamiltonian.”

  5. The physical source of imprecision in ϕ is left to readers’ imaginations; perhaps it is seismic vibrations, flexibility of the beamsplitters’ mounting brackets, or some other nuisance.

  6. Bob must also assume that detection events for different trials are independent.

  7. If ϕ is the sum of very many independent random variables with finite mean and variance, then this assumption is justified by the central limit theorem.

  8. Diagonalization does not determine the overall phase of each eigenvector, but these phases are arbitrary and do not represent any physically observable quantity.

  9. Unorthodox theories (e.g. Bohmian mechanics or the stochastic-spacetime interpretation) may consider this information accessible in principle but missing from quantum theory.

  10. A discrete distribution is degenerate iff its support consists of exactly one value.

  11. Jaynes’ original papers on subjective statistical mechanics address this issue [18].

  12. The usual method of MaxEnt quantum thermodynamics is: given a Hilbert space and a set of expectation values {〈F i 〉}, define an equilibrium mixture \(\bar{\rho}_{T}\) as the density operator which maximizes S vN −∑λ i F i 〉. Here {〈F i 〉} is called a macrostate and {λ i } are Lagrange multipliers. The von Neumann entropy of \(\bar{\rho}_{T}\) is then identified with S T for that macrostate [15].

References

  1. Eddington, A.S.: The Nature of the Physical World. Macmillan, New York (1927)

    Google Scholar 

  2. Carroll, S.: From Eternity to Here: The Quest for the Ultimate Theory of Time. Penguin Group, New York (2010)

    Google Scholar 

  3. van der Zouw, G., Weber, M., Felber, J., Gähler, R., Geltenbort, P., Zeilinger, A.: Aharonov-Bohm and gravity experiments with the very-cold-neutron interferometer. Nucl. Instrum. Methods Phys. Res. A 440, 568 (2000)

    Article  ADS  Google Scholar 

  4. Chapman, M., Ekstrom, C., Hammond, T., Rubenstein, R., Schmiedmayer, J., Wehinger, S., Pritchard, D.: Optics and interferometry with Na2 molecules. Phys. Rev. Lett. 74(24), 4783 (1995)

    Article  ADS  Google Scholar 

  5. Nairz, O., Arndt, M., Zeilinger, A.: Quantum interference experiments with large molecules. Am. J. Phys. 71(4), 319 (2003)

    Article  ADS  Google Scholar 

  6. Gerlich, S., Eibenberger, S., Tomandl, M., Nimmrichter, S., Hornberger, K., Fagan, P.J., Tüxen, J., Mayor, M., Arndt, M.: Quantum interference of large organic molecules. Nat. Commun. 2, 263 (2011)

    Article  Google Scholar 

  7. Zeilinger, A.: General properties of lossless beam splitters in interferometry. Am. J. Phys. 49(9), 882 (1981)

    Article  ADS  Google Scholar 

  8. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28, 4 (1949)

    Google Scholar 

  9. von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)

    MATH  Google Scholar 

  10. Oliver, W., Yang, Y., Lee, J., Berggren, K., Levitov, L., Orlando, T.: Mach-Zehnder interferometry in a strongly driven superconducting qubit. Science, 9 December (2005)

  11. Collin, E., Ithier, G., Aassime, A., Joyez, P., Vidon, D., Esteve, D.: NMR-like control of a quantum bit superconducting circuit. Phys. Rev. Lett. 93(15), 157005 (2004)

    Article  ADS  Google Scholar 

  12. Martinis, J.M., Nam, S., Aumentado, J., Lang, K.M.: Decoherence of a superconducting qubit due to bias noise. Phys. Rev. B 67, 094510 (2003)

    Article  ADS  Google Scholar 

  13. Martinis, J.M., Cooper, K.B., McDermott, R., Steffen, M., Ansmann, M., Osborn, K.D., Cicak, K., Seongshik, Oh., Pappas, D.P., Simmonds, R.W., Yu, C.C.: Decoherence in Josephson qubits from dielectric loss. Phys. Rev. Lett. 95, 210503 (2005)

    Article  ADS  Google Scholar 

  14. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379 (1948)

    MathSciNet  MATH  Google Scholar 

  15. Jaynes, E.T.: Information theory and statistical mechanics II. Phys. Rev. 108(2), 171 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  16. Jaynes, E.T.: Gibbs vs Boltzmann entropies. Am. J. Phys. 33, 391 (1965)

    Article  ADS  MATH  Google Scholar 

  17. Kuić, D., Županović, P., Juretić, D.: Macroscopic time evolution and MaxEnt inference for closed systems with Hamiltonian dynamics. Found. Phys. 42, 319 (2011)

    ADS  Google Scholar 

  18. Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106(4), 620 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Joos, E., Zeh, H.D., Kiefer, C., Giulini, D.J.W., Kupsch, J., Stamatescu, I.-O.: Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edn. Springer, Berlin (2003)

    Google Scholar 

Download references

Acknowledgements

This paper was inspired by discussions of Wheeler’s delayed-choice experiment with Prof. Robert Gilmore and graduate student Allyson O’Brien at Drexel University. Additional discussion and examples of decoherence arising from an averaging process can be found under the heading “fake decoherence” in [19].

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sam Kennerly.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kennerly, S. Illusory Decoherence. Found Phys 42, 1200–1209 (2012). https://doi.org/10.1007/s10701-012-9664-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-012-9664-6

Keywords

Navigation