Article
Simultaneous wave and particle knowledge in a neutron interferometer
City College of the City of New York, New York, NY 10031, USA
Physics Letters A (Impact Factor: 1.68). 04/1988; 128(8):391394. DOI: 10.1016/03759601(88)901144 ABSTRACT
We give a measure of particle knowledge in a neutron interferometer that reflects one's ability to predict in which beam a neutron is located. We can measure wave knowledge by contrast of the interference pattern. Then one's simultaneous knowledge of both is determined by a single parameter (not an uncertainty relation), running from full particle to full wave knowledge. We extend the discussion to partially coherent beams. Our measure of information is much simpler than the conventional one.

 "(Mohd Asad Siddiqui), tabish@ctpjamia.res.in (Tabish Qureshi) acterizes the extent to which one can distinguish which of the two slits the particle passed through by a quantity D, and the visibility of the interference by V. Then the relation putting a bound on the two is given by the socalled EnglertGreenbergerYasin (EGY) duality relation [3] [4] "
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ABSTRACT: The issue of interference and whichway information is addressed in the context of threeslit interference experiments. A new path distinguishability D Q is introduced, based on unambiguous quantum state discrimination. An inequality connecting the interference visibility and path distinguishability, V + 2D_Q/(3−D_Q)Q ≤ 1, is derived which puts a bound on how much fringe visibility and whichway information can be simultaneously obtained. It is argued that this bound is tight. For twoslit interference, we derive a new duality relation which reduces to Englert’s duality relation and the Greenberger–Yasin duality relation, in different limits. 
 "An indication of the importance of the WZ analysis is indicated by the interest it has attracted from numerous authors, who, based on the WZ analysis developed particlewave duality relations. The first such relation was introduced by Greenberger and Yasin (GY) [13], with further developments in references [49] [50] [51] [52] [53] [54]. Detailed derivations followed, the most notable by Jaeger, Shimony and Vaidman (JSV)[49], and then by Englert [53]. "
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ABSTRACT: I argue that quantum optical experiments that purport to refute Bohr's principle of complementarity (BPC) fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particlewave duality relations, which evolved from the WoottersZureck reformulation of BPC (WZPC). I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need to consider the meaning of particlewave duality relations and to question their fundamental status. I further argue (albeit, in opposition to BPC) that particle and wave complementary concepts are on a different footing than other pairs of complementary concepts. 
 "Much later, this principle was made quantitatively precise by deriving a bound on to what extent the two natures could be observered simultaneously, independently by Greenberger and Yasin[3] and Englert[4]. Here one characterizes the extent to which one can distinguish which of the two slits the particle passed through by a quantity D, and the visibility of the interference by V. Then the relation putting a bound on the two is given by the socalled EnglertGreenbergerYasin (EGY) duality relation[3] [4] V 2 + D 2 ≤ 1. (1) "
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ABSTRACT: The issue of interference and whichway information is addressed in the context of 3slit 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 whichway information can be simultaneously obtained. It is argued that this bound is tight. For 2slit interference, we derive a new duality relation which reduces to Englert's duality relation and GreenbergerYasin's duality relation, in different limits.
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