QUANTUM BOOK. Imaginary non-local forms of future reading. Abstract. EPR Nonsense.

Transcription

1 QUANTUM BOOK Imaginary non-local forms of future reading Michael A Popov Oxford UK Michael282eps@gmailcom Abstract Quantum computer is a new generation of computers based on entirely different physics and mathematics Because Nature uses this sort of superior computational devices (for example, human brain is natural non-classical or quantum computer), we believe that quantum computation is reachable for humans and one day we could be readers of completely futuristic quantum books of the next generation,indeed Today s quantum practitioners use thought experiments and pure laboratory experiments in order to develop approximations to our quantum future Even without real prototype of quantum computer, mathematicians developed experimental forms of software for future quantum computers ( Peter Shor and Len Grover algorithms, for example ) and this success may suggest that we can make similar attempts in futuristic studies of the books of the quantum future as well My article is an attempt of this kind of quantum anthropology of the quantum ebook, used mathematical imaginary experiments, understandable protocols and elementary complex algebra which can help us not only to aware quantum reality of the future but also to become participant of the most advanced scientific adventure of the 21 st century Key Words : quantum, EPR, complex numbers,reading EPR Nonsense In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen [1] for the first time in the World History of Nonsense translated famous quantum paradox on observer dependent reality into the experimentally verifiable conclusions of a crucial thought experiment We may describe today such EPR-experiment (in later David Bohm's terms ) as an impossible experiment where a particle with no spin ( with no magnetic circular movements described by imaginary numbers ), while at rest, decays into two identical particles ( labelled 1 and 2), each with spin 1/2 Since momentum is conserved, the particles fly out in opposite directions And since spin is conserved, the two spins must add up to zero Therefore, in good agreement with right science, if the spin of particle 1 is measured to be up along some specific direction, then the spin of particle 2 must be down' along some specific direction and there is no such thing as observer dependent spin at all Following the results of such sort of EPR experiment, it became obvious that any observer dependent reality, predicted by quantum theorists in s, is simply a nonsense In the mid-1960s, however, mathematician and experimentalist John Bell ( CERN ) showed that it was actually quite possible to realize the EPR-experiment, when the two particles are emitted with definite spin directions, which are locally fixed at the decay These directions, according to Bell, nevertheless, might be Unknown to the experimentalist He then showed that if we measure the spin of particle 1 along one direction, and the spin of particle 2 along another direction, the results will be correlated For instance, if we measure the spin of both particles along the same direction, particle 2 will always have the spin down when particle 1 has the spin up Thus, a nonsense, described by Einstein - Podolsky - Rosen in 1935 ( in which strong correlations are observed between presently no interacting particles, even if

2 they are detected arbitrarily far away from each other ) became a part of experimental physics! Being mathematician, John Bell formulated his findings in the terms of Bell s inequality or equation which suggests that if the particles are independent of each other like classical objects ( in Newton Einstein s physics) then the measurement will satisfy the inequality If the particles are not independent of each other, ie they are Entangled particles (hence, new term Entanglement of modern physics ), then Bell s inequality fails Since Bell's discovery, a number of physical tests have been performed successfully [by J Clauser and S Freedman (1972), A Aspect, J Dalibard, and G Roger (1982), and G Weihs, Ch Simon, T Jennewein, H Weinfurter, and A Zeilinger (1998)] [2] Moreover, in 21 st century whole new non-nonsensical physics with their ideas of quantum computers, quantum telepathy, quantum internet, quantum teleportation, quantum cryptography, quantum banks, quantum markets, quantum elections, quantum space communications and even new quantum information philosophy and anthropology are emerged It is quite natural, in this context, to continue this list of unprecedented discoveries of new quantum theory and my article is the first attempt of investigation of imaginary forms of quantum reading inspired by Bell s discovery and used nontraditional in social sciences mathematical thought experiments, understandable protocols and elements of complex algebra which can help us not only to aware quantum reality of the future but also to become participant of the most exciting scientific adventure of the 21 st century Quantum Computer Quantum computer is a new generation of computers based on entirely different physics and mathematics the first proposed by Yuri Manin and Richard Feynman in 1982 Because Nature uses this sort of superior computational devices (for example, Human brain is natural non - classical or quantum - like computer ), theorists believe that quantum computation is reachable for humans and one day we could be readers of completely futuristic quantum books of the generation 2 +, indeed In comparison with classical computer which I use to print this text, quantum computer can perform some impossible operations based on impossible entanglement of quantum particles and molecules For example, beyond conventional mathematical knowledge, quantum computer can use two-dimensional or complex numbers (sometimes called imaginary ) Hence, as consequence, quantum computer uses not conventional classical bits ( bit,here, is a way of denoting True or False statements ) of information, but qubits expressed by pure spatial complex numbers In some sense, it is perfectly Strange Mathematics, because qubit represents another kind of modern mathematics, where all imaginary numbers and spaces ( Hilbert complex vector space ) are no more imaginary, in any ordinary sense of the word, than a real mathematical objects Speaking more exactly, qubit is so-called complex root ( -1) of the elementary magic equation z² + 1 = 0

3 This is true magic completely unsolved equation, because the equation has no real ( special term for conventional one-dimensional numbers ) roots It is easy to see that, nevertheless, since z² = -1, we can use special symbol i for -1 And quantum computer scientists use such sort of impossibility i = - 1 in order to translate the bits of classical information into the qubits of quantum information indeed Another mysterious characteristic of qubit concept is necessary to think about quantum information by a pair of numbers, united symbolically, for purpose of technical convenience, in the form a + bi ( or 0 + 1i ) when True ( symbolically 1 ) and False ( symbolically 0 ) can Coexist Simultaneously at the Same Time in the state of superposition 0 + 1i It is very difficult to explain rationally in the terms of everyday logic And quantum computer scientists use geometrical visualization in order to explain it For example, the pair of numbers (False,True ) or ( 0,1 ) in superposition i= 0 + 1i may be represented pure geometrically by a point in a plane or by the displacement (0,1) Hence, some unbelievable logical operations for quantum computer are formulated In particularly, such puzzling operation as Square Root of Not (!) is perfectly performed by quantum computer In the context of our complex symbolism, we can explain it pure mathematically as ( 0,1 ) ( 0, 1 ) = ( -1, 0 ) It is surprisingly, but such kinds of classically impossible logical operations became possible today Experimental physicists use photons, trapped ions and nuclear spins to realize such sort of square roots of Not in laboratory Because search of suitable hardware for quantum computer are faced now with technical unsolved problems, there are merely few established companies in the world - D-Wave Systems, Magic G, Id Quantique and SmartQuantum - which attempt to find best human approximation to real quantum computers in metal Despite of hardware difficulties, mathematical software of quantum computers is well developed area of quantum computations in 2010s [3] Even without real prototype of quantum computer, mathematicians developed experimental forms of software for future quantum computers ( for example, Peter Shor algorithm demonstrating advanced results in the search of the prime numbers, L Grover n algorithm used in particular by Google in the search of databases ) and this success may suggest that we can make similar attempts in futuristic studies of the books of the quantum future as well Quantum Book Modern ( classical ) book is a written or printed work presenting by text ( or electronic text by e-reader ) and consisting of pages glued or sewn together usually along one side Correspondingly, Quantum Book could be defined as an electronic version of a printed book that can be read on a quantum computer or handheld quantum device ( by generation 2+ ) designed specifically for this purpose Even without prototype of quantum computer, today we can describe this kind of future book purely mathematically as futuristic approximation in the following form As is known both Classical and Quantum computers use binary numeral system to represent electronic information Base-2 number system usually consists of two digits : 1 and 0 It is very easy and practical arithmetic, because it is obvious that 1 + 1

4 = 10, 1 1 = 1, 0 1 = 0, 1/0 = 0 and 1 /1 = 1 Computers adopt that simplicity to perform massive amount of information in bits and qubits In order to translate English text into base-2 number system we may use some mathematical algorithms ( say, Gray code ) and ASCII ( American Standard Code for Information Interchange ) Thus, for example, in ASCII to say BOOK 20 means , and to say + 6 means , etc Let word It contains 8 bits ( = 1 BYTE ) of classical information However, in contrast with classics every state for an 8-qubit system for quantum computer is given by writing already 2^8 = 256 complex numbers (!) Thus, elementary 8 qubits of quantum information need Complex Vector Space having counter-intuitively merely 256 dimensions : 0+1i, 0+1i,0+1i,0+1i,0+1i,0+1i,0+1i,0+1i ( complex number 0 ) 0+1i, 0+1i,0+1i,0+1i,0+1i,0+1i,0+1i,1+0i ( complex number 1 ) 0+1i,1+0i,1+0i,0+1i,1+0i,0+1i,1+0i,0+1i ( complex number 106 ) 0+1i,1+0i,1+0i,0+1i,1+0i,0+1i,1+0i,1+0i ( complex number 107 ) 0+1i,1+0i,1+0i,0+1i,1+0i,0+1i,0+1i,0+1i ( complex number 108 ) 0+1i,1+0i,1+0i,0+1i,1+0i,0+1i1+0i,0+1i ( complex number 254 ) 0+1i,1+0i,1+0i,0+1i,1+0i,0+1i1+0i,1+0i ( complex number 255 ) Or, shortly: (c0) (c1) (c106) (c107) (c108) (c254) (c255) Correspondingly, quantum computer with only just 64-qubit register, one would need to store 2^64 = complex numbers and generally speaking n- qubit register could be written by 2^n complex numbers

5 This means in particular, that our simple word of some future quantum page of X quantum book may contain 256 contexts, which are able to express our + 6 word in at least 255 languages at the same time as well as to offer the most suitable context according with the taste, the knowledge, the personal characteristic of the reader Moreover, this facts can suggest that for quantum text it is not necessary to indicate the state of each bit of a byte at all, qubits of information are in different states before and after reading Thus, process of quantum reading itself cannot be finished at all And, after every reader, quantum book could be changed dramatically and forever We may await, hence, that every new page of quantum book can be associated with colossal information relocations, new references to quantum memory of every book and new sophisticated navigation tools ( based may be on Grover-like algorithms ) for successful quantum reading In order to realise such sort of reading, probably, a new level of computational decoding of the text is needed Indeed, in the world of classical books, reading or decoding of the text with n symbols is required 8n bits ( in our case )of information, whereas quantum reading of the same text needs already 256 states of n contexts or 256n qubits of information If it is true, then quantum reading of some advanced generation will be the most luxury and the most sophisticated pleasure of everyday human life in future Pure mathematically, we may also deduce that reading of n -1 or n + 1- pages is able to change a state of all possible structures ( register ) of the quantum book, actually Thus, understanding of a whole could be reached by random reading of the random pages in general Hence, what is impossible for classical reader ( for example, to find single book with complete atomic 10³² bits description of human anatomy or even 10 Gigabytes description of the fully 3-dimensional structure of a human to a 1 mm³ resolution, etc ) can be quite possible for quantum reader Quantum Libraries An existence of future quantum libraries seems to be justified by modern experiments with future quantum internet and we can use scientific results ( Sept 2012 ) in our approximations to future forms of quantum reading As is known, the quantum internet (the next generation information processing platform, promising secure communication and an exponential speed up in distributed computation) is based on possibility of quantum teleportation It is interesting that by using quantum teleportation of the quantum states (not real objects! ) unknown quantum states from quantum device (of the reader) can be transferred over arbitrary distances to quantum libraries whose location is Unknown Thus, location of library ( libraries ) perhaps is not very important in future and correspondingly all imaginary forms of quantum reading could be, definitely, nonlocal This means that reader s search cannot be connected with closer ( in geographical sense ) library but it could be performed by network of libraries whose location is unknown Another finding of experimentalists is that quantum libraries can use classical as well as quantum channel of communication associated in future with classical and quantum internet In order to imagine hypothetical library visit by future quantum

6 reader, let us assume that future quantum teleportation should be based also on the simultaneous creation of at least three photons ie teleportation needs three parties communication say, reader ( Charlie ), P-library s librarian ( Alice ) and T- library s librarian ( Bob ) connected by classical and quantum internet channels Hence, following last results of the experiments with quantum teleportation over 143 km using active feed-forward by researchers from Vienna [4], we may imagine library visit in future, when reader Charlie prepares the text 1 for teleportation using some single-photon source Some Einstein-Podolsky-Rosen like source generates an entangled pair of texts 2 and 3 Then, librarian Alice performs a Bell-state reading ( measurement ) on of the texts 1 and 2, Alice projects texts onto of the four Bell s states and sends the result via the classical feed - forward channel to librarian Bob The text 3 is sent via the free-space quantum internet to Bob, who applies a unitary transformation on text 3 and thus turns its state ( state of the text ) into a replica of the initial quantum state Quantum teleportation, thus, is realized and after such sort of perfectly personalized and secure communication reader Charlie is able to use simultaneously biggest data of two unknown libraries in order to finish his book Some elementary mathematical description of our library visit could be presented in the following manner: # Reader Charlie provides the input text 1 to be teleported to librarian Alice in a state φ = α + β, where α, β are complex numbers and α² + β² = 1 # Librarian Alice : putting α² + β² = 1 = (α² + β² ), Alice projects texts onto : α= + [ ½ { (α² + β² ) + α }] α= - [ ½ { (α² + β² ) + α }] β= + [ ½ { (α² + β² ) - α }] β= - [ ½ { (α² + β² ) - α }] # Librarian Bob : the quantum channel is used by Alice and Bob to share the entangled state β= + [ ½ { (α² + β² ) - α }] which is simple consequence of Alice s solution of the magic equation z² = α + βi Personalized Quantum Archives As is known, quantum teleportation potentially may be considered as suitable strategy for Mind Uploading through quantum states teleportation [5] Indeed, in some general sense, mind uploading is assumed an existence and possibility of Quantum Internet, Quantum Libraries, Quantum Secure Communications and Personalized Quantum Archives ( PQA ) in future Because we have now good experimental approximations to quantum internet and quantum libraries, well-developed quantum cryptography and quantum private

7 communication theory, it seemed development of PQA and Mind Upload could have sufficient foundation today Mind uploading ( as well as whole brain emulation, substrate independent minds ) is usually defined as some hypothetical processes of transferring considerable majority of the mental contents from a particular human brain into a different substrate, most commonly an engineered substrate such as a digital, analogue or quantum computer [6] Current experiments with quantum teleportation, however, may suggest another kind of approach for Mind Uploading when it is assumed that there is Plato Descartes s hypothetical Innate Mathematical Memory ( IIM card ) realized by Dialogue between quantum libraries ( toy- memory ) and Personality ( clone memory ) Such sort of Digital Nativism is similar with memory uploading concept and it could be based on advanced quantum technique of quantum teleportation, advanced singlephoton sources, EPR-like generators of entangled pairs, ultra-low-noise single photon detectors, free-optical quantum and classical internet links, and, probably, entanglement-assisted clock synchronization Invitation This article is the first attempt to focus solely on contemporary and experimental manifestations of a new kind of concept of future book that can be classified as Quantum Book 2+ I regard the article as being really elementary and I hope that it may be useful as an invitation in the new brave world of Quantum Media

8 References [1] Einstein,A, Podolsky,B & Rosen,N Can quantum-mechanical description of physical reality be considered complete? PhysRev 47, (1935) [2] Popov,MA In Defence of Quantum Idealism Physics- Uspekhi Russian Academy of Sciences,46 (12), (2003) [3] Williams,CP Explorations in Quantum Computing ( Springer Publisher )(2011) [4] Xiao-Song,M,Herbst,T,Scheidi,T,Wang,D, Kropatschek,S, Naylor,W,Wittmann, B, Mech,A,Kofler,J, Anisimovs,E,Makarov,V,Jennewiin,T,Ursin,R,& Zeilinger,AQuantum teleportation over 143 kilometres using active feed-forward Nature, 13 September, vol 489, (2012) [5] Astakhov,V& Astakhov,TBrain prostheses as a dynamical system ArXiv (physics) (2007) [6] Goerizel,B,& Ikle,M Special issue on mind uploading Introduction International Journal of Machine Consciousness, vol l4, (1),1-3 (2012)