1. prepared by Huriye Gürsel
Chapter#2 – Part II
prepared by Huriye Gürsel

2. Evolution vs. Evolution Theory
Evolution: mechanism which can be observed, just like gravity. We feel gravity all the time, but to be able to observe evolution, one needs to investigate species and their characteristics deeply!
Evolution Theory: We require theories for being able to understand how the “evolution” process has been taking place.
I believe evolution is valid.
I don’t believe evolution is valid Discuss!
I believe evolution theory is valid.
I don’t believe evolution theory is valid.

3. Evolution vs. Evolution Theory

4. Hypothesis vs. Theory A theory is shaped by a hypothesis.
Hypothesis is NOT equal to assumption or proposition!
Hypothesis also needs to “satisfy” the conditions which needs to hold true for a method to be called scientific.

5. Hypothesis vs. Theory
If the hypothesis satisfies all criteria and cannot be falsified, also strengthens itself via solid evidences, then the hypothesis turns into a theory.
It is developed for understanding the mechanism behind the things that are already known to be existing, and are supported by solid evidences!

6. Darwin’s Observation

7. Darwin… Darwin was not an atheist.
He didn’t form his theory as an opposition to religion.
He only aimed to explain a mechanism he had noticed to be occurring as a result of the deep research he had been conducting for so long.
He only defined natural selection and explained how species change in time!

9. Darwin… His conclusive remark:
“If a living thing manages to live long enough to be able to reproduce, s/he possesses the most suitable characteristics for achieving to continue this existence and delivers these characteristic properties to other generations. As time passes by, these properties spread within the population and the ones not providing such an advantage get extinct.”

12. Information for Non-living Systems
The basic concept of information, its importance, and the similarities and differences between classical and quantum information.
Classical information theory and its application to communication.
Quantum mechanics and communication based on the laws of quantum mechanics.

13. Information…
During the second half of the 20th century, the development of computer science led to a new way of understanding physics—in very general terms, physical systems can be thought of as computers processing information.
The initial state of a physical system is the input to a computer and evolves as the computer performs computations to some final state, which is the computer’s output. Studying physics in this way not only allows us to use the tools of theoretical computer science and information theory to understand physical laws, but also provides us with an entirely new way of thinking about physics—we can think of the values of the physical attributes of a system as information held in that system.

14. Information…
On the other hand, the fact that physics and computation means that the laws of information processing depend fully on the laws of physics. This means that whenever we discover new laws of physics, the laws of computation will most likely also be affected in a very profound way.

15. Classical vs. Quantum Computers
Classical Computers:
Binary Code
Def. Any code that uses just two symbols to represent information.
The way that most computers and computerized devices ultimately send, receive, and store information.
Quantum Computers:
Atoms encode information. Single charged atoms are quantum bits (qubits)

16. Strange Quantum Effects
You can be at two different places at the same time!
You can move backward and forward
simultaneously!
You can tunnel through the walls!
SPOOKY!!

17. Bit vs. Qubit
For further details, you may watch .

18. Different Ways of Expressing Information
HURIYE

19. Can you express your name via binary coding?

20. I can be at the left and right at the same time
Why Quantum Computing
Billions of years would be required with a classical computer!
Quantum physics explains everything about us. Not powerful enough! Can simulate dynamics of these systems hence so powerful!
State: an object in state 0 me standing at the left
An object in state 1 Me standing at right
I can be at the left and right at the same time

21. Coin Experiment - Entanglement
If these two coins were entangled you would get same result
Individually entirely random series of zeros and ones!
But both of you would get exactly same pattern!
Spooky action at a distance!

22. Classical Information Theory
Classical information theory assumes that information evolves according to the laws of classical (Newtonian) physics (the pioneers of information theory did not even make this assumption explicitly —it was just there naturally, because classical physics is very intuitive)
Quantum information theory assumes that information is represented by quantum states and allowed to evolve according to the laws of quantum mechanics.

23. Classical Information Theory
Initially it was thought that geometry is part of mathematics until Einstein showed that geometry is determined by gravity in the universe.
In order to determine what kind of geometry we live in, we need to measure angles and distances in our vicinity (i.e. We need to study the physics of General Relativity).
Now, a century after Einstein’s great insight, we understand that logic, information, and computation are not parts of mathematics only, but also belong to physics. How much information we can store and how quickly we can process it depends upon the laws of physics .

24. Shannon Information
Shannon modeled information as events which occur with certain probabilities. He postulated the following requirements that any measure of information must possess:
The amount of information in an event x must depend only upon its probability p.
I(p) is a continuous function of p Continuity is a desirable quality for physical quantities (disregarding phase transitions and some other anomalies). In this case, the continuity condition says that if the probability of an event changes by a very small amount, the information contained in that event changes by only a small amount.
I(px,py)=I(px)+I(py)

25. Postulates of Quantum Mechanics
There are four postulates of quantum mechanics which are said to describe all we need to know about quantum systems (i.e. the four postulates can be used to describe any quantum system):
• States. States of physical systems are represented by vectors in Hilbert spaces. This postulate says that a physical state in a quantum system can be represented as one of the vectors |. in the Dirac notation defined above.
• Observables. Observables are represented by Hermitian operators. This is because these operators have real eigenvalues, which are appropriate for representing physical quantities (such as an amount of energy, or a distance from the Sun, for example).
• Measurement. A quantum state can be measured by use if a set of orthogonal projections.
• Unitary Evolution. Any change that takes place in a quantum system which is not a measurement can be expressed by the action of a unitary operation.

26. Quantum Information
Information is often thought of as an abstract quantity which has nothing to do with the physical world. However, information reaches us through interaction with the outside world and is stored and processed in our bodies, which are—as far as we know—fully subject to the laws of physics. We can draw two crucial insights from this:
• Information must be encoded into a physical system.
• Information must be processed using physical (dynamical) laws

27. Bits or Qubits?
The first striking difference between quantum and classical information storage is that we cannot clone “unknown” quantum states.
“No cloning” implies that there is a limited amount of information which we can learn about an unknown quantum state. This is in stark contrast to classical physics: we can always learn everything about a classical system even if we have only one copy of it, simply because classical measurements are noninvasive and do not destroy the state of the measured system. For example, when we photocopy a piece of paper, we do not destroy the content of the writing on it.

28. Quantum Communication Method #1: Quantum Cryptography, BB84 cryptography protocol
Cryptography is a process by which two parties, Alice and Bob, can communicate secretly. “No cloning” is a vital ingredient in quantum cryptography as it prevents an eavesdropper from copying the quantum states that Alice and Bob send to one another. The main issue in cryptography is how to establish a secret key between Alice and Bob. This is a string of zeros and ones which is in the possession of both parties, but is not known to any other unwanted parties—that is, eavesdroppers (see Fig. 3.1). Once Alice and Bob have a secret key, they can use it to communicate secretly and exchange any other messages. Establishing this secret key is—as far as we know— impossible to do in an unconditionally safe way within the laws of classical physics.

29. Figure...

30. Quantum vs. Classical Information
We can consider classical information theory as a subset of quantum information theory where we are restricted to orthogonal states. In this view, there is no division between the classical and quantum worlds. When we talk about classical communication, we mean quantum communication which does not use the superposition principle.

31. Quantum Information
How can quantum information be characterized? We usually think of information as being classical — in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the basis of this argument, conclude that quantum information can never exist and we can only have access to classical information. It turns out, however, that quantum information can be quantified in the same way as classical information using Shannon’s prescription. It can be shown that there is a unique measure (up to a constant additive or multiplicative term) of quantum information such that
• S is purely a function of the probabilities of outcomes of measurements made on a quantum system (i.e. a function of a density operator);
• S is a continuous function of probability;
• S is additive

32. So,What Next?

33. Acknowledgements Biology Chemistry
I would like to express my sincere appreciation to the ones stated below for helping me throughout preparation of these notes.
Biology
Miss Huriye Ünvan (Molecular Biologist) for her valuable explanations on DNA and structure of chromosomes & Mr. Ahmet Gürsel (Veterinary undergrad, 4th year) for further discussions on the DNA coding and for providing me with great sources regarding the topic.
Chemistry
Mrs. Cebriye Gürsel for her help in grasping ideas regarding the molecular structures.

34. Sources Used A Universe from Nothing, Lawrence Krauss
Quantum Fluctuations & Life, Davies, 2004 Biosystems 78
Introduction to Quantum Information Science, Vlatko Vedral, Oxford Graduate Texts
An Introduction to Thermal Physics, Daniel V. Schroeder
Introduction to Quantum Information Science, Masahito Hayashi,Satoshi Ishizaka,Akinori Kawachi,Gen Kimura, Tomohiro Ogawa