Bargmann invariants and local unitary equivalence

2026/07/18 by Minghui Ma, Rui Shi · 1 citation
#quant-ph #math.OA

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Abstract

In this paper, we study the local unitary equivalence of quantum states on ℂⁿ⊗ℂⁿ, which is an important notion in quantum information theory. For the case n=2, the local unitary orbits of two-qubit states are completely determined by their local unitary Bargmann invariants. We show that the local unitary Bargmann invariants do not form a complete set of invariants of local unitary orbits for n\geqslant 3, which negatively answers a problem proposed by L. Zhang and B. Xie.

Citations

• The invariant theory of n × n matrices
• Completely positive linear maps on complex matrices

Cited by

• Revisiting the invariant ring of two-qubit mixed states

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