不可比状态的分类
A classification of incomparable states
摘要：
设（|>，|（）（）（）|联系\nleftrightarrow|））、\emph，即，(|），（|不能通过局部变换和经典通信（LOCC）以概率1相互转换。我们发现，不可比的状态可以是多拷贝可转换的，\emph，即，可以存在\emph{k}，使得（|n> ^{ \otimes k+1} \to| n> ^{ \otimes k+1}），即，（k+1）的副本（|1、可以将（k+1）个拷贝转换为（|1、以概率论为基础，以（|> ^{ \otimes n} \nleftrightarrow| n> ^{ \otimes n} \forall n \leq k）。我们称这种状态为\emph{k} -拷贝LOCC不可比状态。我们提供了一个必要条件，使一对给定的状态是\emph{k}拷贝LOCC的一些\emph{k}无与伦比的。我们还表明，存在的状态，既不是\emph{k}拷贝LOCC无与伦比的任何\emph{k}，也催化，即使有多个副本。我们称这种状态为强烈的不可比拟的。给出了强不可比性的一个充分条件。我们证明了涉及许多拷贝的决定性转化的最佳概率（p_{max}（|> ^{ \otimes m} \to|即使源态具有\otimes纠缠熵，也可以随着源态的数量（m）而指数地减小。
英文摘要：
Let (\{| ψ> ,| ϕ>}) be an incomparable pair of states ((| ψ\nleftrightarrow | ϕ>)), \emph, i.e., (| ψ>) and (| ϕ>) cannot be transformed to each other with probability one by local transformations and classical communication (LOCC). We show that incomparable states can be multiple-copy transformable, \emph, i.e., there can exist a \emph{k}, such that (| ψ> ^{\otimes k+1}\to | ϕ> ^{\otimes k+1}), i.e., (k+1) copies of (| ψ>) can be transformed to (k+1) copies of (| ϕ>) with probability one by LOCC but (| ψ> ^{\otimes n}\nleftrightarrow | ϕ> ^{\otimes n} \forall n\leq k). We call such states \emph{k}-copy LOCC incomparable. We provide a necessary condition for a given pair of states to be \emph{k}-copy LOCC incomparable for some \emph{k}. We also show that there exist states that are neither \emph{k}-copy LOCC incomparable for any \emph{k} nor catalyzable even with multiple copies. We call such states strongly incomparable. We give a sufficient condition for strong incomparability. We demonstrate that the optimal probability of a conclusive transformation involving many copies, (p_{max}(| ψ> ^{\otimes m}\to | ϕ> ^{\otimes m})) can decrease exponentially with the number of source states (m), even if the source state has \emph{more} entropy of entanglement.
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