Quantum States and the Density Matrix

Gui‐Lu Long

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.

Maurice A. de Gosson

Jing Li

At first,the concept of quantum bit,the density matrix and Bloch vector were introduced.Then by using the outer product——mathematical tools,the density matrix of single quantum bit,the mixed state quantum bit and the related properties were discussed.Based on the matrix operator theory,the pure states,mixed states;entangle state,the superposition states and the density matrix were analysed.The researching results contributed to the deep understanding of quantum theory.

Yong Heng Zhou

We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum entanglement, unless the density matrix has the form $ρ_{AB}=ρ_A\otimes ρ_B$.