Qubits as hypermatrices and entanglement

2024/04/02 by Isaac Dobes, Naihuan Jing · 1 citation
Computer Science · Mathematics · #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture #Tensor decomposition and applications

paper · pdf · doi:10.1088/1402-4896/ad3989

Abstract

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 π -transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of 2 n -qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of 2 n -qubits in terms of the n -tangle.

Citations

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Tensor slice rank and Cayley's first hyperdeterminant

Cited by

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

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