Local Unitary Equivalence of Generic Multi-qubits Based on the CP Decomposition

Chang, Jingmei; Jing, Naihuan

doi:10.1007/s10773-022-05106-w

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2022

2024

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Cited by 2 publications

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“…For the last few decades, classifying entangled states has been a major endeavor for researchers in theoretical quantum information [1][2][3][4]. For bipartite quantum systems, the theory of entanglement is well understood and established [5], however for multipartite systems, the very notion of entanglement is still being worked out [6][7][8][9]. As such, much of the focus has been on better understanding and expanding the theory of entanglement in multipartite systems [6].…”

Section: Introductionmentioning

confidence: 99%

Qubits as hypermatrices and entanglement

Dobes,

Jing

2024

Phys. Scr.

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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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