Alternative fidelity measure between 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, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)

Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)[05/04105-5]

Brazilian Millennium Institute for Quantum Information,

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)

Australian Research Council