[MUSIC] This days if you have ever heard the word quantum, probably you have also heard quantum information. What is quantum information? This is what we will be discussing this week. But before that let me comment that, when we are studying quantum information, we will study some systems which probably you are not familiar with, why? This is because there are two approaches to study quantum mechanics. The one approach is starting from the most familiar object and another approach is to start from simpler objects. If you read textbooks, they may choose different starting point. And this is pretty different compared to a lot of other physical systems that if you study them, the familiar and simple objects usually the same for a lot of physical systems. But for quantum mechanics is not the case. The familiar objects for example, the position and the momentum of me, okay, this is familiar. So you can imagine what if I become smaller and study a quantum version of me. What is the position and what is the momentum? However this is familiar but is actually pretty complicated mathematically, why? Because position and momentum can take a lot of values and can take continuously a lot of values. So that introduces a lot of mathematical difficulties. To study quantum information which is more complicated things, we'd like to study with simpliest possible set up. And that corresponds to simplest objects. But the simplest objects which doesn't have classical counterpart. What I mean actually I mean spin, if you know speed. Okay, so this is some sort of angular momentum without rotating, okay. Classical you cannot imagine that object but it is existing quantum mechanically. And if you don't know I will show you what spin looks like. So in quantum information we will start with very simple in mathematical science, very simple objects but it is very unfamiliar. So this is why in the beginning part from the very beginning of quantum mechanics, we are studying familiar objects. To trying to build up some intuition before studying this simple but have no classical counterpart objects, what is the nature of this simple objects? Imagine again about Alice in her quantum wonderland When Alice is observing the electrons, she finds that electron has two states. The electron can stand upwards and can stand hand down If the electron is hand standing and superposition with the same electron which is standing then what do you get? You will get an electron which is lying, all right. Have you seen anything like this before in our classical intuitions? And if Alice is going to study the relation between a few electrons, she finds that although she has very good memory, a really good memory. However, if she studies the relation between a handful of electrons, like five or 10, then she finds it's a nightmare, is impossible to understand what is going on there. And even worse Alice finds that the relation between these electrons not only complicated, but also superluminal, faster than light. What do I mean, if one electron is here, another electron is light years away. In this situation, the relation between this electrons, there are some quantum information, I will specify what they are. There are quantum information in it. And if I change the state of one electron here, immediately, the quantum information between this electron and the electron so far away, light years away. Immediately changes, the change speed is faster than the speed of light. And you may wonder, how this would be possible. Is it in contradiction with special relativity? Finally, suppose Alice is like Einstein that she doesn't want to believe that God play dice. She doesn't want to believe the randomness of quantum mechanics, and she thinks there are some invisible hats, some invisible hidden variables which controls the randomness of particles. Is it possible that will show you in this part that a local version, a simple version of this invisible hidden variable will be ruled out. This is the part of quantum information. Let's get started.
