Trace-Norm Overlaps of Quantum States: Interpolation, Equality, and Data-Processing Rigidity

Zahra Maleki Khouzani, Seyed Mahmoud Manjegani

Let $\rho$ and $\sigma$ be density operators on a separable Hilbert space. For $0<\alpha <1$, we study the directed trace-norm overlap ${\Phi }_{\alpha }(\rho ,\sigma )=\Vert {\rho }^{\alpha }{\sigma }^{1-\alpha }{\Vert }_1$ and its symmetrized form $\math…