Unifying Typical Entanglement and Coin Tossing: on Randomization in Probabilistic Theories
Unifying Typical Entanglement and Coin Tossing: on Randomization in Probabilistic Theories
复制标题
统一典型的纠缠和抛硬币：概率论中的随机化
DOI：
10.1007/s00220-012-1605-x
复制
发表时间：
2011
影响因子：
2.4
通讯作者：
V. Vedral
中科院分区：
文献类型：
--
作者：
Markus P. Müller;O. Dahlsten;V. Vedral
众所周知，纯量子态通常几乎是最大程度地纠缠，因此具有接近最大程度混合的子系统。我们考虑这是否适用于更普遍的概率理论，而不仅仅是量子理论。我们推导出任何概率理论中子系统的预期纯度的公式，其中该数量已明确定义。它适用于纯量子态中的典型纠缠、经典概率论中的抛硬币以及后量子理论中的随机化；简单的概括产生了（反对）对称量子子空间中的典型纠缠。公式准确而简单，仅包含各系统的自由度数和信息容量。它使我们能够以仅依赖于基础理论的粗略属性的方式概括统计物理论证。该公式的证明将几个随机化概念推广到一般概率理论。这包括纯度的概括，有助于最近寻找适当的广义熵度量的努力。
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quantum subspaces. The formula is exact and simple, only containing the number of degrees of freedom and the information capacity of the respective systems. It allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory. The proof of the formula generalizes several randomization notions to general probabilistic theories. This includes a generalization of purity, contributing to the recent effort of finding appropriate generalized entropy measures.