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arXiv:quant-ph/0409092

Detection of incompatible properties without erasure

Nisticó, Giuseppe

Published Sep 15, 2004• 0 citations
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Abstract

In this work we show that in double-slit experiment properties incompatible with Which Slit property can be detected without erasing the knowledge of which slit each particle passes through and without affecting the point of impact on the final screen. A systematic procedure to find these particular properties is provided. A thought experiment which realizes this detection is proposed.

DOI
10.48550/arxiv.quant-ph/0409092

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In this work we show that in double-slit experiment properties incompatible with Which Slit property can be detected without erasing the knowledge of which slit each particle passes through and without affecting the point of impact on the final screen. A systematic procedure to find these particular properties is provided. A thought experiment which realizes this detection is proposed.
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.
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.