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Quantum Device Fabrication Process Engineering

Quantum Zeno-like Paradox for Position Measurements: A Particle Precisely Found in Space is Nowhere to be Found in Hilbert Space

arXiv
Authors: Xabier Oianguren-Asua, Roderich Tumulka

Year

2026

Paper ID

3269

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

Abstract

On a quantum particle in the unit interval [0,1], perform a position measurement with inaccuracy 1/n and then a quantum measurement of the projection |φranglelangleφ| with some arbitrary but fixed normalized φ. Call the outcomes X in[0,1] and Y in\{0,1\}. We show that in the limit n→infty corresponding to perfect precision for X, the probability of Y=1 tends to 0 for every φ. Since there is no density matrix, pure or mixed, which upon measurement of any |φranglelangleφ| yields outcome 1 with probability 0, our result suggests that a novel type of quantum state beyond Hilbert space is necessary to describe a quantum particle after a perfect position measurement.

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  • On a quantum particle in the unit interval [0,1], perform a position measurement with inaccuracy 1/n and then a quantum measurement of the projection |φranglelangleφ| with some...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.19469 [2] arXiv https://arxiv.org/abs/2601.19469 [3] Publisher https://arxiv.org/abs/2601.19469

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