Alternative fidelity measure for quantum states
  We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established. 
Paulo E. M. F. Mendonca, Reginaldo d. J. Napolitano, Marcelo A.   Marchiolli, Christopher J. Foster, Yeong-Cherng Liang