Cite this problem as **Problem 18**.

**Problem**

A little problem introduced in [1] 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, .

**Solution**

The problem has been solved by S. Ishizaka in [2] where it is proven that the bi-negativity is indeed positive for all two-qubit states.

**References**

[1] 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).

[2] S. Ishizaka, »Binegativity and geometry of entangled states in two qubits«, Phys. Rev. A 69, 020301(R) (2004) and quant-ph/0308056 (2003).