# 宏观系统量子纠缠存在么？

薛定谔猫这个理想实验应该是广为人知了。以前人们只是认为这是个理想的东西，是哲学意义上的探讨。可是现在物理学家们已经开始对这个问题进行了深入的研究，它已经是一个很值得探讨的物理问题了。

• 孙昌璞之科普园地
• QUbit上对Quantum Entanglement的介绍
1. S. Ghosh et al., Nature 425 48 (2003).
2. R. Penrose, in A. Fokas et al. (Eds.), Mathematical Physics 2000 (Imperial College, London, 2000).

# Some questions

My boss Prof. Li gave me some questions recently. One of them is whether there is entanglement among the macro-systems. We definitely know that there would be entanglement between the quantum systems, which are micro-scaled. When the system we discussed is too large to be viewed as micro-system, is there entanglement in this system? My boss enlightened me that firstly we should discuss the quantum system, for example, two spins being entangled by a electromagnative wave. We calculate the entanglement between them. Then we add the spin to the system, and calculate the entanglement again. Finally we get the relationship between the entanglement and the number of spins. When the number of spins apoaches to infinity, the micro-system becomes the macro-systems. So we solve the question at the beginning of this entry.

# Entanglement witness

Recently I read a article quant-ph/0503037 written by Marcin Wiesniak, Vlato Vedral and Caslav Brukner. Here is the abstract:

We show that, when measured along orthogonal spatial directions, magnetic susceptibility can reveal entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be universal macroscopic entanglement witness that can be applied independently of the model of the solid (without the knowledge of its Hamiltonian).

The most important result of this article, in my opinion, is the quantum complementary relation. That is the sum of the entanglement and the local properties S=frac{langle rightarrow{M}rangle^2}{N^2}. This article also given a criterion to estimate the solid state system contains entanglement or not. If the magnetic susceptibility bigger than a critical value, there must be entanglement in the system. As we know, susceptibility has been experimental routime for long time. So using the result of the article, we can detect the entanglement in the solid system. I think this is an important result. In fact, this article told us that magntetization only described the local feather of a solid, but susceptibility related with the global entanglement of the solid system.

I guess that the localizalbe entanglment(LE) defined in the recent article PRA 71, 042306 (2005) may have some relation with the result of the article above. The lower bound of LE connects with a correlation function. As we kown, susceptibility is some kind of correlation in the solid system. If I dig deeply in this, I think I can reveal this relation.