论文标题
Choquet积分作为与密度矩阵的近似值，并具有不完整的信息
The Choquet integral as an approximation to density matrices with incomplete information
论文作者
论文摘要
总计$ n $状态$ | i \ rangle $和相应的投影仪$π（i）= | i \ rangle \ langle i | $，在带有$ d $ d $ d $ d $ d $ d $ d $ d $ d $ dimensional hilbert space $ h（d）$的量子系统中。考虑到给定$ p（i）= {\ rm tr} [ρπ（i）] $的部分知名密度矩阵$ρ$（其中$ i = 1，...，n $和n $和$ d \ le n \ le n \ le d^2-1 $）。它用于计算Choquet积分$ {\ cal c}（ρ）$，这是一个积极的半明确遗产矩阵。共音性是形式主义中的一个重要概念，该概念用于使物理相似密度矩阵的模糊概念形式化。结果表明，$ {\ cal c}（ρ）/{\ rm tr} [{\ cal c}（ρ）] $是一个密度矩阵，是与部分已知的密度矩阵$ρ$的良好近似值。
A total set of $n$ states $|i\rangle$ and the corresponding projectors $Π(i)=|i\rangle \langle i|$ are considered, in a quantum system with $d$-dimensional Hilbert space $H(d)$. A partially known density matrix $ρ$ with given $p(i)={\rm Tr}[ρΠ(i)]$ (where $i=1,...,n$ and $d\le n\le d^2-1$) is considered, and its ranking permutation is defined. It is used to calculate the Choquet integral ${\cal C}(ρ)$ which is a positive semi-definite Hermitian matrix. Comonotonicity is an important concept in the formalism, which is used to formalise the vague concept of physically similar density matrices. It is shown that ${\cal C}(ρ)/{\rm Tr}[{\cal C}(ρ)]$ is a density matrix which is a good approximation to the partially known density matrix $ρ$.
