论文标题
Qubit状态空间上的量子剂量等法
Quantum Wasserstein isometries on the qubit state space
论文作者
论文摘要
我们描述了量子位状态空间相对于杰出的成本运营商的弥补等法。我们为涉及所有Pauli矩阵的成本运营商获得了Wigner型结果：在这种情况下，等轴测组由单一或反统一的共轭组成。在Bloch Sphere模型中，这意味着等轴测组与经典的对称组$ \ MATHBF {O}（3）。$相吻合，另一方面，对于由Qubit“ Clock”和“ Shift”运算符产生的成本，我们发现了非主题性和非注射性异构体，超出了常规的异构体。这种现象反映了量子瓦斯汀距离的某些令人惊讶的特性。
We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model, this means that the isometry group coincides with the classical symmetry group $\mathbf{O}(3).$ On the other hand, for the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance.
