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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

New Identity for Cayley's First Hyperdeterminant with Applications to Symmetric Tensors and Entanglement

arXiv
Authors: Isaac Dobes

Year

2025

Paper ID

16428

Status

Preprint

Abstract Read

~2 min

Abstract Words

94

Citations

N/A

Abstract

In this article, a new formula for computing Cayley's first hyperdeterminant in terms of the Levi-Civita symbol is given. It is then shown that this formula can be used to compute the hyperdeterminant of symmetric hypermatrices in polynomial time with respect to their order (assuming fixed side length). Applications to the quantum entanglement of bosons are then discussed. Additionally, in order to obtain the fast calculation of the hyperdeterminant on symmetric hypermatrices, hypermatrix generalizations of elimination and duplication matrices are defined, and explicit formulas for them are derived in the appendix of this article.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • In this article, a new formula for computing Cayley's first hyperdeterminant in terms of the Levi-Civita symbol is given.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2512.03093 [2] arXiv https://arxiv.org/abs/2512.03093 [3] Publisher https://arxiv.org/abs/2512.03093

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