量子力学中的密度矩阵与具有相同密度矩阵的系综的可区分性

Density Matrix in Quantum Mechanics and the Distinction of Ensembles Having the Same Density Matrix

讨论了密度矩阵的不同定义。建议使用完全密度矩阵、压缩密度矩阵和约化密度矩阵分别描写一个封闭量子体系的、一个系综中平均分子的和一个复合体系中的一个子系统的密度矩阵。强调这与现在人们认为的具有相同压缩密度矩阵的系综是完全等价的结论完全不同,具有相同压缩密度矩阵但是成分不同的系综可以通过系综整体测量来区别。作为一个应用,现在认为现有的核磁共振量子计算中没有纠缠的结论是没有根据的。

Density matrix is one important tool in quantum mechanics, and it has very broad applications. However there are different definitions about the density matrix, and they describe quite different systems. There has been some misunderstanding about the density matrix in the community, and these misunderstandings hinder the right application of the density matrix. In this article, we discuss the different definitions of density matrix. We suggest to use the full density matrix, compressed density matrix and the reduced density matrix to describe the state of a complete quantum system, the state of an averaged particle in an ensemble and the state of part of a composite system. We stress that contrary to the wide accepted understanding that ensembles with the same compressed density matrix are physically indistinguishable, they are distinguishable through the so-called ensemble measurement. As an application, we suggest that the present conclusion that the present-day nuclear magnetic resonance quantum computation does not have quantum entanglement is groundless.