Coherence and realism in the Aharonov-Bohm effect

Abstract

The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work, we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results.

13 pages (including appendixes and references), 4 figures. Author's published version

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• Time-symmetry and topology of the Aharonov-Bohm effect
• Two-time quantities as elements of physical reality
• Oracle problems as communication tasks and optimization of quantum algorithms