A characterization of maximally entangled two-qubit states

Abstract

As already known by Rana's result \href{https://doi.org/10.1103/PhysRevA.87.054301}{[\pra {\bf87} (2013) 054301]}, all eigenvalues of any partial-transposed bipartite state fall within the closed interval $[-\frac{1}{2},1]$. In this note, we study a family of bipartite quantum states whose minimal eigenvalues of partial-transposed states being $-\frac{1}{2}$. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is $-\frac{1}{2}$ if and only if such two-qubit state must be maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.

arXiv comment11 pages, LaTeX

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Cited by in corpus (3)

• A characterization of entangled two-qubit states via partial-transpose-moments
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• Positivity and entanglement of polynomial Gaussian integral operators