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arXiv 0907.1784quant-ph
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Entangled states:经典与量子

Entangled states : Classical versus Quantum

S. Kanmani

摘要:

复合系统的量子力学,产生了某些特殊的态,称为纠缠态。一个处于纠缠态的物理系统在它的子系统之间显示出错综复杂的关联。还有一些复合量子态(经典关联态或可分态)没有纠缠。一般认为,纠缠态的这些复杂关联在经典系统中不可能发生,但往往没有严格的证据支持。本文对纠缠态不能在经典力学中产生提供了一个初步的证明。此外,还详细描述了量子系统中纠缠的起源。数学概念,这是必要的,为此目的。在经典环境中没有纠缠是因为复合系统的每个纯经典态都是一个乘积态,即子系统的两个纯态的张量积。相反,有纯复合量子态不能以乘积态的形式表示,甚至不能用乘积态的凸和表示。粗略地说,这是因为经典态是相空间上的正值函数,而量子态是正的线性算子。两个可交换的标值函数空间之间的张量积的结构与两个非可交换的线性算子空间之间的张量积的结构有很大的不同。换句话说,纠缠是一种非对易现象。

英文摘要:

Quantum mechanics of composite systems, gives rise to certain special states called entangled states. A physical system, that is in an entangled state displays an intricate correlation between its subsystems. There are also some composite quantum states (classically correlated states or separable states) that are not entangled. It is generally claimed, often without a rigorous proof to support, that these intricate correlations of an entangled state cannot occur in a classical system. This expository article, provides an elementary proof that entangled states cannot arise in the setting of classical mechanics. In addition, a detailed description of the origin of entanglement in quantum systems is included. The mathematical concepts that are necessary for this purpose are presented. The absence of entanglement in the classical setting is due to the fact that every pure classical state of a composite system is a product state, that is, a tensor product of two pure states of the subsystems. In contrast, there are pure composite quantum states that cannot be expressed in the form of a product state or even by a convex sum of product states. Roughly speaking, this is because classical states are positive valued functions on the phase-space while quantum states are positive linear operators. The structure of the tensor product between two commutative spaces of scalar valued functions is drastically different from that of the tensor product between two non-commutative spaces of linear operators. In other words, entanglement is a non-commutative phenomenon.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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