Abstract
The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${\mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An inequality connecting the interference visibility and path distinguishability, ${\mathcal V} + {2{\mathcal D_Q}\over 3- {\mathcal D_Q}} \le 1$, is derived which puts a bound on how much fringe visibility and which-way information can be simultaneously obtained. It is argued that this bound is tight. For 2-slit interference, we derive a new duality relation which reduces to Englert's duality relation and Greenberger-Yasin's duality relation, in different limits.
Highlights
The two-slit interference experiment with particles has become a cornerstone for studying wave-particle duality
In the following we describe a well established method of unambiguously discriminating between two non-orthogonal quantum states, which goes by the name of Unambiguous Quantum State Discrimination (UQSD) [20,21,22,23,24]
In the analysis carried out in this paper, we have introduced a new path distinguishability
Summary
The two-slit interference experiment with particles has become a cornerstone for studying wave-particle duality. Niels Bohr emphasized that wave-nature, characterized by two-slit interference, and the particle-nature, characterized by the knowledge of which slit the particle passed through, are mutually exclusive [2]. In doing this he raised this concept to the level of a new fundamental principle. Englert characterised the particle nature by the ability to distinguish between the two paths of the particle, by an actual measurement [4] He introduced a quantity D for this purpose, which took values between 0 and 1. Of late there has been a newly generated focus on the three-slit interference experiments [17,18,19], albeit for a different reason
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