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Inferential which-path determination as a test of locality

Ghenadie N. Mardari

Published Dec 2, 2003• 0 citations
OpenAlex

Abstract

Quantum mechanics predicts that which-path information is complementary with fringe visibility in a double-slit interferometer. Traditionally, this was demonstrated on the basis of the assumption that direct path detection necessitates violations of the uncertainty principle. However, there have been recent attempts to prove that uncertainty is subordinated to complementarity and, therefore, fringe visibility should diminish with path-detection even when the uncertainty principle is not violated. This debate can be solved with a simple experimental set-up, which allows for indirect which-path determination.

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Quantum mechanics predicts that which-path information is complementary with fringe visibility in a double-slit interferometer. Traditionally, this was demonstrated on the basis of the assumption that direct path detection necessitates violations of the uncertainty principle. However, there have been recent attempts to prove that uncertainty is subordinated to complementarity and, therefore, fringe visibility should diminish with path-detection even when the uncertainty principle is not violated. This debate can be solved with a simple experimental set-up, which allows for indirect which-path determination.
Einstein's version of the double-slit interferometer is reexamined by taking into account possible degrees of freedom of the detector. This can be considered as a natural generalization of an earlier attempt by Wooters and Zurek, however, it is found that in this approach a new element which is directly related to the uncertainties of physical variables appears and that it affects considerably the visibility of the interference pattern. Thi fact turns out to be a quantitative realization of the complementarity principle in quantum mechanics.
A recent experiment performed by Afshar et al (2007 Found. Phys. 37 295–305) has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information (WPI) in a two-path interferometer. We have reproduced this experiment, using true single-photon pulses propagating in a two-path wavefront-splitting interferometer realized with a Fresnel's biprism, and followed by a grating with adjustable transmitting slits. The measured values of interference visibility V and WPI, characterized by the distinguishability parameter D , are found to obey the complementarity relation V 2 + D 2 ⩽1. This result demonstrates that the experiment can be perfectly explained by the standard interpretation of quantum mechanics.
A recent experiment performed by Afshar et al. has been interpreted as a violation of Bohr's complementarity principle between interference visibility and which-path information a two-path interferometer. The authors have reproduced the same experiment, using true single-photon pulses emitted by a single nitrogen-vacancy (NV) color center in a diamond crystal and propagating in a two-path wavefront-splitting interferometer realized with a Fresnels' biprism, followed by a grating with transmitting slits of adjustable width. The experimental setup is illustrated. The results go far beyond the reported results in the previous works of Afshar et al. and the subtle flaws in their analysis are then pointed out. The measured values of the interference visibility V and the which-path information, characterized by the distinguishability parameter D, are found, with values close to the ideal-case upper bound. This result demonstrates that the experiment can be perfectly explained by the Copenhagen interpretation of quantum mechanics, without any violation of Bohr's complementarity principle.
We revisit the connection between the complementarity and uncertainty principles of quantum mechanics within the framework of Mach–Zehnder interferometry. We focus our attention on the trade-off relation between complementary path information and fringe visibility. This relation is equivalent to the uncertainty relation of Schrödinger and Robertson for a suitably chosen pair of observables. We show that it is equivalent as well to the uncertainty inequality provided by Landau and Pollak. We also study the relationship of this trade-off relation with a family of entropic uncertainty relations based on Rényi entropies. There is no equivalence in this case, but the different values of the entropic parameter do define regimes that provides us with a tool to discriminate between non-trivial states of minimum uncertainty. The existence of such regimes agrees with previous results of Luis (2011 Phys. Rev. A 84 034101), although their meaning was not sufficiently clear. We discuss the origin of these regimes with the intention of gaining a deeper understanding of entropic measures.
Complementarity lies at the heart of conceptual foundation of orthodox quantum mechanics. The wave-particle duality makes it impossible to tell which slit each particle passes through and still observe an interference pattern in a Young's double-slit experiment. In this paper, this duality is appraised under the standard formulation of quantum mechanics for atom interferometers. It is found that the internal freedoms like electronic states of an atom can be used to detect the which-path information of each atom while uphold the interference pattern of atoms when the center-of-mass motion of atoms is detected.
We revisit the connection between the complementarity and uncertainty principles of quantum mechanics within the framework of Mach?Zehnder interferometry. We focus our attention on the trade-off relation between complementary path information and fringe visibility. This relation is equivalent to the uncertainty relation of Schrödinger and Robertson for a suitably chosen pair of observables. We show that it is equivalent as well to the uncertainty inequality provided by Landau and Pollak. We also study the relationship of this trade-off relation with a family of entropic uncertainty relations based on Rényi entropies. There is no equivalence in this case, but the different values of the entropic parameter do define regimes that provides us with a tool to discriminate between non-trivial states of minimum uncertainty. The existence of such regimes agrees with previous results of Luis (2011 Phys. Rev. A 84 034101), although their meaning was not sufficiently clear. We discuss the origin of these regimes with the intention of gaining a deeper understanding of entropic measures.