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Journal of Physics A Mathematical and Theoretical

Ascertaining complementary and incompatible quantum properties by means of double-slit experiments

Giuseppe Nisticò

Published Mar 10, 2008• 6 citations
Publisher

Abstract

The famous two-slits experiment is used to theoretically introduce the problem of detecting both which-slit (WS) property and another quantum property incompatible with the WS one, together with the measurement of the (complementary) position of the final impact point. General conditions for the existence of solutions are singled out, and a family of solutions is concretely found. Moreover, we theoretically design an ideal experiment which realizes this non-trivial detection.

DOI
10.1088/1751-8113/41/12/125302

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The famous two-slits experiment is used to theoretically introduce the problem of detecting both which-slit (WS) property and another quantum property incompatible with the WS one, together with the measurement of the (complementary) position of the final impact point. General conditions for the existence of solutions are singled out, and a family of solutions is concretely found. Moreover, we theoretically design an ideal experiment which realizes this non-trivial detection.
In a typical two-slits experiments we face the question whether it is possible or not to attain knowledge about properties incompatible with Which-Slit property together with the measurement of the final impact point. A wide family of solutions is concretely found and an ideal experiment realizing such a detection is designed, relatively to the detection of three such incompatible properties. In the case of four incompatible properties, general conditions for the existence of solutions are singled out and a particular family of solutions is provided.
In a typical double‐slit experiment, we seek for properties incompatible with Which Slit property, which can be detected without erasing the information about which slit each particle localized on the final screen passed through. It is found that these properties exist if the dimension of the Hilbert space describing the position of the particle is at least 4, but they can have a non‐trivial character only if such a dimension is at least 6. An ideal experiment realizing this non‐trivial detection without erasure is designed.