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.

该研究提出了一种新的量子状态保真度测量方法，利用线性熵和希尔伯特 - 施密特内积计算，具有共同凹性和满足 Jozsa 公设等特殊性质，但不满足乘法可加性和单调性，并且还确定了密度矩阵空间的新度量方法和 Uhlmann-Jozsa 保真度在量子比特状态下的共同凹性。