具有相同纠缠和局部酉等价的量子态
Quantum states with the same entanglement and local unitary equivalence
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中文总结 AI 辅助
本文指出LOCC可互转换性不等同于LU等价，并给出充分条件：对于具有完全纠缠维数（以Schmidt数向量量化）的多体态，LOCC互转换性仅在LU等价下成立。
中文摘要 AI 辅助
由经典通信辅助的局部操作（LOCC）在纠缠理论的资源理论化表述中扮演着基础性角色，它在纠缠态集合中引入了一种具有操作意义的排序。LOCC中局部酉（LU）变换这一特定类别显然在求逆运算下是封闭的。因此，LU等价态可以通过LOCC相互转换，因而具有相同的纠缠量。为此，LU等价性在纠缠理论的背景下已被深入研究。然而，正如我在此用一个简单例子指出的，其逆命题并不成立：存在一些纠缠态，它们可以通过LOCC相互转换，但并非LU等价。这促使我们研究在何种条件下，LOCC可互转换性可由LU等价性来表征。我为此提供了一个充分条件。当考虑具有完全纠缠维数（以Schmidt数向量量化）的多体态时，LOCC可互转换性只能在LU等价性下成立。
英文摘要
Local operations assisted by classical communication (LOCC) play a fundamental role in the resource-theoretic formulation of entanglement theory inducing an operationally meaningful ordering in the set of entangled states. The particular class within LOCC of local unitary (LU) transformations is obviously closed under inversion. Thus, LU-equivalent states are interconvertible by LOCC and have therefore the same entanglement. For this reason LU-equivalence has been thoroughly studied in the context of entanglement theory. However, as I note here with a simple example, the converse is not true: there exist entangled states that are interconvertible by LOCC but which are not LU-equivalent. This motivates studying under which conditions LOCC interconvertibility is characterized by LU-equivalence. I provide a sufficient condition for this to hold. When one considers multipartite states with full entanglement dimensionality (as quantified by the Schmidt number vector) LOCC interconvertibility can only hold under LU-equivalence.
发表机构
- Universidad Carlos III de Madrid（马德里卡洛斯三世大学）
- Instituto de Ciencias Matemáticas (ICMAT)（数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
