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Edited by Peter J. Rossky, The University of Texas at Austin, Austin, TX, and approved July 15, 2014 (received for review January 16, 2014)
Significance
In 2012, Menzel et al. reported on the results of a fundamental experiment raising questions regarding the simultaneous observation of wave-like and particle-like properties in a given quantum system. Whereas the general applicability of the duality principle to entangled subsystems is an open question, we bring the current understanding of the duality principle a step forward by theoretically deriving the strongest relations between the visibility of an interference pattern and the which-way information in a two-way interferometer such as Young’s double slit. This formalism successfully describes tests of duality where postselection on a subset of the interference pattern is applied. Our analysis even reconciles the surprising results of Menzel et al. with the duality principle in its standard form.
Abstract
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that “the simultaneous observation of wave and particle behavior is prohibited” [Scully MO, Englert B-G, Walther H (1991) Nature 351:111–116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality.
Footnotes
- ↵1To whom correspondence should be addressed. Email: eliot.bolduc{at}gmail.com.
Author contributions: E.B., J.L., and R.W.B. designed research; E.B. and J.L. performed research; E.B. and F.M.M. contributed new reagents/analytic tools; E.B. analyzed data; and E.B., J.L., F.M.M., G.L., and R.W.B. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1400106111/-/DCSupplemental.
Apparent violation of duality
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