Quantum Information, Quantum Computation’s Implications to Cognition

1. Quantum Information, Quantum Computation’s Implications to Cognition • Guolin Wu • Prof. Ph.D. • Vice Dean, School of Marxism • Director, Research Center for Philosophy • of Science and Technology • South China University of Technology • Guangzhou 510640, P. R. China • 11/01/2016

2. Related Background of Wu • BOOKS: • AnIntroduction of philosophy of physics (2007); • Philosophy of Quantum Information (2014). • Philosophy of Quantum Technology(2016)

3. The Cognition Science is one of the disciplines which develop rapidly recently, but it has not included features of quantum mechanics into its reaches by now. Quantum information theory based on quantum mechanics has risen since the 1990s; it also brings inspirations to the cognition science. This paper will introduce quantum information, quantum entanglement, and quantum computing briefly, and then explores their implications to cognition.

4. Outline of my paper • 1. Quantum Information • 2. Quantum Entanglement • 3. Features of Quantum Computation • 4. The implication to cognition

5. 1. Quantum Information • the current classic information uses bit as information unit. In classic context, bit only has one state as 0 or 1. • A bit is the information quantity which gives a value of a classic two-value system. In physics, a bit is a two-value system, and it can be made as one of two distinguishable states, for example, true of false, 0 or 1. Classic information could be described by classic physics, without need for quantum mechanics.

6. A quantum system includes great amount of micro-particles, and in quantum mechanics, it is described by quantum states. The Schrödinger equation describes evolution of quantum states • In the quantum communication theory, the unit of quantum information is named “qubit”. A qubit is a two-state system; moreover, the two states are linearly independent from each other. Generally speaking, the two basic quantum states are marked by Dirac symbols: |0> and |1>

7. Qubits |0> and |1> are vectors in two dimension plural space, they are arbitrary superposition states of two-state system. For instance： and • a and b are pluralities.

8. Schrödinger Cat:half live and half death

9. Using quantum state to present information is the first step to research quantum information. As soon as using quantum state to present information, the “quantization” of information has been realized. • Accordingly, principles of quantum physics must be obeyed: evolution of information obeys Schrödinger equation, transmission of information is right the transmission of quantum state in quantum channel, and the extraction of information is quantum measurement to quantum system. • In laboratory, physical carrier of qubit could be any kind of two-state system, like orthogonal polarization of photons, spin of electrons, and energy level of atoms or quantum particles.

10. Compared with classic information which lay its basis on classic physics, quantum information is based on quantum mechanics. Quantum information extends information from classic areas into quantum domain; this enriches the meaning of information. We can define the philosophical meaning of quantum information as follow: • quantum information is not quantum reality, but the showing of states, correlations, changes, and differences of quantum reality (Wu, 2006).

11. the Main Features of quantum information： • （1）Quantum information has the property of coherence . Quantum coherence is also a kind of integrity; it unifies local freedom and global correlation . Classic information does not havethe coherence. • The coherence refers, when wave is being transmitted, some kind of related feature between its physical quantity in different position and different time, this property is generated by change of wave’s phrase.

12. Coherence happens between these quantum states, and that is quantum coherence.

13. e.g. double-slit experiment

14. （2）Quantum entanglement • if one state of composite system can not be written as direct product of the pure state of its two sub-systems, it’s an entanglement state. Quantum entanglement makes transmission of quantum information non-local, which is impossible for classic information.

15. （3）No-cloning of quantum information • The quantum cloning refers that an exactly same state is generated in another system, without change of the original quantum state. Cloning is essentially different with transmission of quantum state. Quantum transmission means a quantum state disappears in original system, and shows up in another system. Of course, the principle of quantum non-cloning does not forbid non-strict cloning of quantum state. For comparison, classic information can be cloned completely.

16. （4）Quantum information can not be deleted completely • Quantum information is different from classic information. It has been proved that complete deletion of any unknown quantum state is impossible. • Apparently, this is an important different feature between quantum information and classic information. This may means that, quantum information is more objective than classic information, which can be deleted completely.

17. （5）Quantum information processes in internal space, and it changes much more rapidly than classic information. • By contrary, classic transmits in four-dimension space-time, and its speed is no more fast than light. The so-called internal space is the space which is generated by the internal variable (spin, for example) of micro particles. In laboratory, quantum information has been successfully transmitted in spin-space.

18. Outline of my paper • 1. Quantum Information • 2. Quantum Entanglement • 3. Features of Quantum Computing • 4. The implication to cognition

19. 2. Quantum Entanglement • In 1935, A. Einstein, B. Podolsky and N. Rosen pubilished a paper which also included the notion of entanglement. They proposed a quantum related state of two particles in the above so-called EPR paper：

20. The definition of Quantum Entanglement • the wave function (probability amplitude) can not represented as the direct product of wave functions of its sub-systems, then it is an entanglement state.

21. |00>+|11> can not • satisfy with： The above state is an entangled state.

22. In principle, any two-particle system could have quantum entanglement, such as atom system, ion system, and photon system. There are many ways to make entanglement state in experiments, besides entanglement state with two particles, there are entanglement state with three particles and so on.

23. At last of this section, we introduce quantum teleportation briefly. Quantum entanglement is the key point of quantum teleportation.

25. the particle 1 will be transmitted which has a unknown quantum state a and b be are unknown coefficients.

26. For transmitting particle 1, micro-particle 2 and 3 must be in an entanglement state. Regardless how long the distance between 2 and 3 is, as soon as the Bell-basis joint measurement towards 1 and 2 is made, coefficients a and b will be transmitted to particle 3 immediately. And particle 3 will have a state. • which is the same as quantum state of particle 1.

27. Outline of my paper • 1. Quantum Information • 2. Quantum Entanglement • 3. Features of Quantum Computation • 4. The implication to cognition

28. From perspective of physics, computer is a physics system. Quantum computer is a quantum mechanics system. Process of quantum computing is evolution of quantum state of quantum mechanics system; it includes manufacturing, evolution and measurement of physical state. • Actually, classic computing is based on classical physical understanding towards state of coding and computing process. However, quantum computing is based on quantum mechanics understanding towards state of coding and computing process.

29. 3. Features of Quantum Computation • （1）Quantum memory device has immense memory ability. • According to classic information theory, as for a two-value system,（0, 1）, if the probability of one value is 1/2, then information quantity determining value of this system is one bit. For n two-value system, there are n-bit binary numbers totally , everyone of them share the same probability, so information quantity for specifying one is n bits. That is to say, a classic bit only can not be manufactured on two of two logical states, 0 or 1, but one for once.

30. 经典信息，每个位置仅存储1个2进制数，即 总体表示一个数，即十进制的5。 1 0 1 0，1 0，1 0，1 量子信息，每个位置可存储0或1两个数，即每个位置可存储2数，那么，共有3个数，就可以存储23个数。如果有n个位，可存储2n个数。 illustration of memory

31. However, a qubit can be manufactured on the coherent superposition state of 0 and 1, that is to say, it can memory 0 and 1 meanwhile. • For a quantum memory device with n qubit, ideally speaking, it can memory the superposition state of 2n number, but in classic case, just one of them.

32. （2）Quantum computation has parallelity. • Parallelity of quantum computing is determined by parallelity of quantum algorithm. • One operation of quantum computer to n quantum memory device, that is doing mathematical operations to 2n data at the same time. This equals that classic computer operates times repeatly, or operate with different processors.

33. As M. Nielson points out: parallel property is one of fundamental feature of quantum algorithm, in brief, quantum parallel property make quantum computer calculate values of f(x) for many different x at the same time.

34. 经典计算机 只能出现1+1+1=3 量子计算机可能出现 1+1+1<3或1+1+1>3 Classic vs. quantum computers

35. （3）quantum computation is in whole. • But classic computation is local.

36. （4） Some quantum algorithms have abilities of acceleration. • In 1994, Peter Shor from AT&T Company invented the Shor algorithm, which is also called quantum algorithm with “Shor Factorization of large numbers” • For example, for a factorization of a 60-bit decimal number, it will take 1017 seconds by using a classic super computer with a speed of 1012 times/seconds, almost life of the universe. Under quantum computing, we only need 10-8 seconds.

37. Outline of my paper • 1. Quantum Information • 2. Quantum Entanglement • 3. Features of Quantum Computing • 4. The implications to cognition

38. 4. The implications to cognition • Cognition science is based on the classic science, and quantum mechanics and quantum information theory are beyond classic science. Here we discuss the implications of quantum information, quantum entanglement and quantum computation for cognition.

39. 4.1 The formal syntax or rules are objective, with real content, not purely formal or syntactic.

40. Searle's Chinese Room • The formal syntax or rules are objective, with real content, not purely modal or syntactic. Searle’s put up his famous Chinese Room ideal experiment. Imaging Tom (reading or understanding only in English) was held in an enclosed room, and was given a number of Chinese books, but he does not know Chinese. Then, supposing after those Chinese books, he was given the second batch of the Chinese books with a set of rules (written in English), and these books have relationships with those of first batch.

41. Therefore, when Tom answered exactly like a Chinese-speaker did, he passed the Turing test, but he could not handle any Chinese. For native speakers, Tom acted like a computer, for Tom did not understand any Chinese, what he did was just operating according to rules. Thus, Searle came to the conclusion that computer has no real intelligence, that is to say, computer couldn’t think.

42. Searle put up his famous Chinese Room with ideal experiment. • In short, Searle's Chinese Room ideal experiment’ s basic ideas as follows: • ① Computer program is a formal syntax or rules; • ② Consciousness has spirit content (or semantic meanings); • ③ syntax and semantics are different, and syntax is not adequate enough to have semantic meaning. Therefore, it’s impossible for computer has any consciousness.

43. Searle's Chinese Room • The rules of these books were written in English. taking advantage of these rules, Tom could link one group of symbols with the other. Assuming again, given the third batch of Chinese symbols, Tom would be able to relate the third group of symbols with the former two groups by using these rules, and had the ability to transmit the Chinese symbols outside the room. If Tom didn’t know the third group of documents contained the questions of the man outdoor, he would never know that the symbols he transmitted were the answers. Obviously, Tom was dealing with some formal symbols, without learning any Chinese.

44. Just as Searle put it, "The digital computer concept is that its operations can be pure formal statement." "Symbols do not make any sense, they do not have semantic content; they do not involve anything. They can be established only by forming the structure or syntax.” • To the understanding of Searle, man has intelligence, in that human has intentionality.

45. In the classical computer, the rule does not have the objectivity or real content. BUT It is a wrong impression. • In fact, computer programming is not a pure form or pure syntax. It appears that in the quantum computer, Quantum computer program or rules (quantum algorithm) are restricted by quantum mechanics rule or the objectivity of quantum world. It is not arbitrary. Quantum computation rules has semantics, and the contents of it can't break laws of physics, because the computer is a physical system, it must be in accordance with the laws of physics operation.

46. 4.2 Quantum information cannot be completely remove. • this means that quantum information is objective at some degree, rather than subjective information. Therefore we proposed that a minimum of objective quantum information unit is a quantum bits. Similarly, quantum information not fully cloning, this explains some quantum information is not be completely replication.

47. Combining quantum information no-cloning and no-deleting, this means that there are not be processed parts of quantum information, or the quantum information also has the characteristics of "information encapsulation".

48. Obviously, this has some similarities with Fodor's "information encapsulation ". Fodor thought that Perception module possesses the characteristics of information encapsulation, and is not affected by the object of cognitive processing ways of understanding. • However, classical information is continuous, and can completely remove, classical information does not have "information encapsulation" characteristics. Although classical information is the showing of classical reality, but is weaker reality than the quantum information.

49. From the point of quantum information, there is the smallest information unit in cognition. Quantum information must rely on quantum object or quantum reality.This was similar with the embodiment, because people's cognitive ability is based on the brain activity.

50. 4.3 Cognition may be non-local. • For two microscopic particles of quantum entanglement, these two particles are in a whole state, but also has a degree of separation. • For identical twins, it is made of the same zygote. The zygote forms two or more embryos. Monozygotic twins from the same zygote, and accept exactly the same chromosomes and genetic material, so as their gender and appearance, and the like. It is very common for them to be ill at the same time .