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arXiv · 2312.06944

Qubits as Hypermatrices and Entanglement

Isaac Dobes·Naihuan Jing
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Abstract

In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $\pi$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle.

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Isaac Dobes, Naihuan Jing. 2023-12-12. Qubits as Hypermatrices and Entanglement. https://doi.org/10.1088/1402-4896%2Fad3989

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