We derive a generalized wave-particle duality relation for arbitrary multi-path quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a novel quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle, for multi-path quantum interference, can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-know complementarity relation. The new duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
We consider issues related to tachyonic inflation with exponential potential. We find exact solution of evolution equations in the slow roll limit in FRW cosmology. We also carry out similar analysis in case of Brane assisted tachyonic inflation. We investigate the phase space behavior of the system and show that the dust like solution is a late time attractor. The difficulties associated with reheating in the tachyonic model are also indicated.
A quantitative measure of quantum coherence was recently introduced, in the context of quantum information theory. This measure has also been propounded as a good quantifier of the wave nature of quantum objects. However, actually measuring coherence in an experiment is still considered a challenge. A procedure for measuring coherence in a multi-slit interference is proposed here. It can be used for experimentally testing duality relations for interference experiments involving more than two slits.
Bohr's principle of complementarity, in the context of a two-slit interference experiment, is understood as the quantitative measures of wave and particle natures following a duality relationHere D is a measure of distinguishability of the two paths, and V is the visibility of interference. It is shown that such a relation can be formulated for N−slit or N−path interference too, with the proviso that the wave nature is characterized by a measure of coherence (C). This new relation, D 2 + C 2 ≤ 1 is shown to be tight, and reduces to the known duality relation for the case N = 2. A recently introduced similar relation (Bagan et al., 2016) is shown to be inadequate for the purpose.
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