Abstract
Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path information to quantify the particle property. However, coherence is the core and basis of the interference phenomenon. If we could use coherence to characterize the wave property, the understanding of wave-particle duality would be strengthened. A recent theoretical work [ Phys. Rev. Lett.116, 160406 (2016)] found two relations between quantum coherence and path information. Here, we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people's understanding of coherence and provide a new perspective regarding wave-particle duality.
Highlights
Bohr’s complementarity principle is at the heart of quantum mechanics
The particle property of the photons can be characterized by path information using minimum-error state discrimination and by the mutual information between detector states and the outcome of the measurement performed on them; the wave property of the photons can be characterized by the coherence in the l1 measure and relative entropy measure using the tomography of the target state
We demonstrate the relation between the coherence in l1 measure and the path information [28]
Summary
Bohr’s complementarity principle is at the heart of quantum mechanics. The core of this principle is that an object has multiple properties and that these properties cannot, in theory, be measured simultaneously [1, 2]. The quantified coherence can be used as a generalization of the interference visibility to characterize the wave property of a particle inside a multipath interferometer, which would provide a new perspective to quantify wave property and deepen the understanding of the quantum coherence and wave-particle duality Until now, these new measure of wave-particle duality relations have not yet been demonstrated experimentally. The particle property of the photons can be characterized by path information using minimum-error state discrimination and by the mutual information between detector states and the outcome of the measurement performed on them; the wave property of the photons can be characterized by the coherence in the l1 measure and relative entropy measure using the tomography of the target state. This entropic version of the coherence-path information duality relation in the case of two-path will be demonstrated in the following experiment
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