Qubits as Hypermatrices and Entanglement

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.

11 pages; New title and revised version

References in corpus (10)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
• A potential multipartide entanglement measure
• Local Unitary Classification of Arbitrary Dimensional Multipartite Pure States
• Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence
• SLOCC Invariants for Multipartite Mixed States
• Local Unitary Invariants for N-qubit Pure State
• Quasi multipartite entanglement measure based on quadratic functions
• Local unitary equivalence of generic multi-qubits based on the CP decomposition
• Higher order singular value decomposition and the reduced density matrices of three qubits

Cited by in corpus (1)

• Local Unitary Equivalence of Tripartite Quantum States In Terms of Trace Identities