Some reflections on my "work" at NUS, Centre for Quantum Technologies.
I hadn't realised it then, but coming up with something there is quite a difficult thing to do. I'm not sure if those people that my prof had previously recruited before they started uni had produced anything, but it is not a nice feeling to hang around at a place for five months without much idea of what's going in. I guess an analogy would be like being employed by a greek company in greece, with all the books(except maybe one) that teach greek also written in greek.
To be more specific, my journey started with my prof asking me to do the exercises in Griffith's Intro to QM (or as the taiwanese grad student would call it, the 猫书), and learning about Perez-Horodecki's criterion for separable states. Then he taught me about pure states and mixed states. One week later, I was given one 4 page paper, which supposedly requires me to understand a 90 page review paper on quantum entanglement before I could appreciate it. I got stuck on the fifth page, i.e, when the first mathematical equation appeared (the definition of a separable state). It was written in Dirac's notation and made use of the tensor product symbol. It was around that time when I started chapter 3 in the 猫书, where Dirac's notation was taught in one page. (I don't think I'm the only one who can't learn Dirac's notation explained in one page) But there wasn't any mention of tensor products, so I tried to learn about it on Wikipedia, which was a really bad idea, since I followed every link, hoping to be able to understand this one by following the next... but it somehow got into group theory and abstract algebra. Having learnt nothing about tensor products (except the fact that it's a bilinear map), I tried to see if it was related to tensors. I didn't manage to learn much about tensors. After two weeks of struggling with Dirac notation and the elusive tensor product, I asked my prof what a tensor product is, and he gave a really simple explanation. Lesson learnt: don't know, ask. Around this time, a teacher happened to ask me how I was doing, and he recommended me Susskin's lecture and Cohen-Tannouji's textbook, which were really helpful.
Around this time, my prof asked me to help him write some lecture notes for grad students, and I got really excited, cos it made it sound like I was very zai. I came up with the first set of lecture notes, but honestly, I don't think I really understood the material well enough to write notes about it, so my notes were quite crap. Perhaps his intention was to make me think hard about what I was learning. But a nice side effect was that I got introduced to LaTeX, which is NOT user friendly at all.
Just when I thought I could be helping those after me to learn about quantum information, I realised that Nielson and Chieng's textbook of quantum information was better than what I could ever write in the next few months, so the notes I wrote was quite redundant. Also, in the last week there, I realised that measures of quantum entanglement had to be associated with some application for it to have any physical meaning, and so far I had learnt nothing about the application. There have been a few instances when people asked me "can you explain in lay-man's terms what is it that you do?" and I couldn't. At the end of it, I didn't even understand half of that 90 page review paper. That sucks.
But oh well. At least I learnt some LaTeX and linear algebra. And I finally have some idea of what a matrix determinant is.
