- Letter
- Open Access
Decoherence implies information gain
Phys. Rev. Research 7, L012040 – Published 24 February, 2025
DOI: https://doi.org/10.1103/PhysRevResearch.7.L012040
Abstract
It is shown that if the wave function of a quantum system undergoes an arbitrary random transformation such that the diagonal elements of the density matrix in the decoherence basis associated with a preferred observable remain constant, then (i) the off-diagonal elements of the density matrix become smaller in magnitude, and (ii) the state of the system gains information about the preferred observable from its environment in the sense that the uncertainty of the observable is reduced in the transformed state. These results do not depend on the details of how the system-environment interaction generates the random state transformation, and together imply that decoherence leads, in general, to information gain, not information loss.
Physics Subject Headings (PhySH)
Article Text
References (22)
- S. L. Adler, Why decoherence has not solved the measurement problem: A response to P. W. Anderson, Stud. Hist. Philos. Sci. Part B: Stud. Hist. Philos. Mod. Phys. 34, 135 (2003).
- L. Ballentine, Classicality without decoherence: A reply to Schlosshauer, Found. Phys. 38, 916 (2008).
- E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I. O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed. (Springer, Berlin, 2003).
- M. Schlosshauser, Decoherence and the Quantum-to-Classical Transition (Springer, Berlin, 2010).
- M. Schlosshauer, Quantum decoherence, Phys. Rep. 831, 1 (2019).
- W. H. Zurek, Quantum theory of the classical: Einselection, envariance, quantum Darwinism and extantons, Entropy 24, 1520 (2022).
- W. H. Zurek, Quantum Darwinism, Nat. Phys. 5, 181 (2009).
- W. H. Zurek, Decoherence and the transition from quantum to classical, Phys. Today 44(10), 36 (1991).
- E. Joos and H. D. Zeh, The emergence of classical properties through interaction with the environment, Z. Phys. B 59, 223 (1985).
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2006).
- T. Heinosaari and M. Ziman, The Mathematical Language of Quantum Theory (Cambridge University Press, 2012).
- N. Gisin, Stochastic quantum dynamics and relativity, Helv. Phys. Acta 62, 363 (1989).
- D. C. Brody and L. P. Hughston, Lévy models for collapse of the wave function, J. Phys. A: Math. Theor. 56, 125303 (2023).
- S. L. Adler, D. C. Brody, T. A. Brun, and L. P. Hughston, Martingale models for quantum state reduction, J. Phys. A: Math. Gen. 34, 8795 (2001).
- H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993).
- H. W. Wiseman and L. Diósi, Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems, Chem. Phys. 268, 91 (2001).
- D. Williams, Probability with Martingales (Cambridge University Press, 1991).
- A. N. Kolmogorov, Foundations of the Theory of Probability (Chelsea Publishing Company, New York, 1956), English translation of A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung (Ergebnisse Der Mathematik, 1933).
- D. C. Brody and A. J. Trewavas, Biological efficiency in processing information in green plants, Proc. R. Soc. London A 479, 20220809 (2023).
- A. Peres, Classical interventions in quantum systems. I. The measuring process, Phys. Rev. A 61, 022116 (2000).
- S. L. Adler, Derivation of the Lindblad generator structure by use of the Ito stochastic calculus, Phys. Lett. A 265, 58 (2000).
- D. C. Brody, Quantum formalism for the dynamics of cognitive psychology, Sci. Rep. 13, 16104 (2023).
