[MUSIC] Is this time to summarize, I'm going to summarize the course with what you have done and what you haven't done. So, we started from the course by summarizing quantum theory and quantum theory is presented as a framework of information processing. Quantum states means preparation of quantum system and quantum dynamics means quantum process and quantum measurement means readout. And then quantum system is explained in terms of cubic. So, cubit is a unit of information processing. So, by cupid we could quantify the quantum information or information properties of quantum systems. Two cubits presented and two cubits contain interesting property is called entanglement correlations which do not have crista counterpart. And also this entire state is consequence of C NOT gates and quantum interactions. Interestingly if we have a quantum gates that generate to cubit states and single cubit states then we can prepare any type of quantum states. And we can construct or approximate any type of quantum circuit which is quantum computation. This means that universality appears from two cubit interaction and single cubic operation. So, then based on this structure we apply cubit and to keep it to communication, and computation. Any computation, we looked at quantum algorithm and which can be interpreted as an information processing, and Vegas dimension like different quantum algorithms. So that was the deutsch’s algorithm and Deutsch’s algorithm can be seen as a quantum challenges communication or face estimation. And or the free transformations as well, so we have looked at quantum computation and then we characterized quantum channels, it's a self system dynamics. So, that described quantum communication and then we found that entanglement is actually key resource. That key resource in quantum communication quantum computation. So entitlement means the capability of realizing seen at gates and entanglement is related to the secret property of quantum china. And moreover use the entire with entanglement we can overcome the limitations in the distribution of quantum states. So, by a common swapping or uncommon swapping in quantum repeat quantum state distributed over this fixed distance here. And here it can be connected to increase the communication distance twice and just congratulating maximum entire state maximum interest at all. In all notes we can have you can establish a long distance quantum communication. So, these are the topics and from fundamentals, and a key element of quantum information processing. We didn't discuss about other types of quantum collisions. So, in quantum information there are other types of quantum collisions called quantum stealing and non locality. So, I didn't explain other types of quantum coalition, but they all these contemplations have interesting property to quantum cryptography, or random number generations and etc. And also what I didn't explain here is a quantum error correction. This is similar to entanglement distillation, so we had a role makes the state into pure entanglement state, is a way of removing the classical no is contained in quantum state. And quantum error correction does exactly the same thing. So, quantum correlation, because in reality quantum systems are so fragile that they interact with the environment. Then often what we meet is this channel and the quantum error correcting code. The goal is to convert this one to identity channel. So, if we want so this guy want to remove all quantum noise. So, it's very important technique to perform quantum computation in a clear manner to get really the quantum advantages. And also to fact arise any third party interrupt to quantum channel. This is also useful technique, but we didn't cover this one. But to realize this content and creating code. Well there is a there is also a requirement for how to wear, so to realize QECC. The realization of quantum gate must be of high precision. This may not be feasible with current technologies according to quantum technologies. So, what a feasible is short time interaction. So, we could generate quantum dynamics for short time and then maybe contaminated them. So, this is this kind of technique is called a NISQ. It's noisy internet and scalable quantum, so we could prepare 50 or 30, so some number of cubits, but some noises contained over there. And also quantum operations are limited. However the working principle behind it is quantum, so therefore, applying this one. Maybe it is possible to get certain quantum advantages. So, this quantum algorithms the examples will be QA or A and 3QE. So yeah, the topics would be very interesting, but we didn't have a chance to discuss about them. But okay. But this quantum error correcting code and needs to algorithms and quantum relations, and all these. I mean, these are practical or application or even fundamental. And all these sides in fact based on save the fundamental understanding on quantum systems, and dynamics, and entanglement.