论文标题
扩大资源量词添加性的概念
Enlarging the notion of additivity of resource quantifiers
论文作者
论文摘要
每当物理数量成为实现有用任务必不可少的必不可少的时，就需要定义适当的措施或单调量子来量化它。在量子力学中，连贯性，纠缠和贝尔非局部性是此类数量的例子。给定一个量子状态$ \ varrho $和量词$ {\ cal e}（\ varrho）$，两者都任意，确定$ {\ cal e}（\ varrho^{\ otimes n}）$是一项困难的任务。但是，如果优点$ \ cal {e}的$结果是加性的，那么我们只有$ {\ cal e}（\ varrho^{\ otimes n}）= n e $，带有$ e = {\ cal e}（\ cal e}（\ varrho）$。在这项工作中，我们通过内部产品$ {\ cal e}（\ varrho^{\ otimes n}）= \ vec {n} \ cdot \ cdot \ vec {e} $，其中$ \ vec {e} =（ E}(\varrho^{\otimes i_2}),\dots,{\cal E}(\varrho^{\otimes i_q}) )$ is a vector whose $q$ entries are the figure of merit under study calculated for some numbers of copies smaller than $N$ ($1 \le i_1<i_2<\dots <i_q <n $），其中$ \ vec {n} =（n_ {i_1}，n_ {i_2}，\ dots，n_ {i_q}）$，是一串数字，仅取决于$ n $，以及一组整数$ \ \ \ \ \ \ {i_j} $。我们表明，可以通过这种增强的添加性来定量地近似某些球形对称状态的一击可蒸馏的纠缠。
Whenever a physical quantity becomes essential to the realization of useful tasks, it is desirable to define proper measures or monotones to quantify it. In quantum mechanics, coherence, entanglement, and Bell nonlocality are examples of such quantities. Given a quantum state $\varrho$ and a quantifier ${\cal E}(\varrho)$, both arbitrary, it is a hard task to determine ${\cal E}(\varrho^{\otimes N})$. However, if the figure of merit $\cal{E}$ turns out to be additive, we simply have ${\cal E}(\varrho^{\otimes N})=N e$, with $e={\cal E}(\varrho)$. In this work we generalize this useful notion through the inner product ${\cal E}(\varrho^{\otimes N}) = \vec{N}\cdot \vec{e}$, where $\vec{e}=({\cal E}(\varrho^{\otimes i_1}), {\cal E}(\varrho^{\otimes i_2}),\dots,{\cal E}(\varrho^{\otimes i_q}) )$ is a vector whose $q$ entries are the figure of merit under study calculated for some numbers of copies smaller than $N$ ($1 \le i_1<i_2<\dots <i_q<N$), where $\vec{N}=(N_{i_1}, N_{i_2}, \dots ,N_{i_q})$, is a string of numbers that depends only on $N$ and on the set of integers $\{ {i_j}\}$. We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.
