Cite this problem as Problem 18.
A little problem introduced in  is the bi-negativity on two qubits: Prove that
holds for every two-qubit state . Here, denotes the partial transpose with respect to the second system (see also problem 2) and is the operator absolute value, .
The problem has been solved by S. Ishizaka in  where it is proven that the bi-negativity is indeed positive for all two-qubit states.
 K. Audenaert, B. De Moor, K. G. H. Vollbrecht, and R. F. Werner, »Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States«, Phys. Rev. A 66, 032310 (2002) and quant-ph/0204143 (2002).
 S. Ishizaka, »Binegativity and geometry of entangled states in two qubits«, Phys. Rev. A 69, 020301(R) (2004) and quant-ph/0308056 (2003).