A broader view on the limitations of information processing and communication by nature

AbstractSeveral new and broader views on computation in Nature and by Nature, and on its limitations and barriers are presented and analysed briefly. Quantum information precessing, global network information processing and cosmology-based information processing theories are seen as three extreme, but well-founded approaches to computation by Nature. It is also emphasized that a search for barriers and limitations in information processing as well as attempts to overcome their barriers or to shift limitations, can have deep impacts on science, especially if they are accompanied by a search for limitations and barriers also in communication and security. It is demonstrated that a search for barriers in communications brings a lot of interesting and deep outcomes. Computational and communication complexity is shown to play an important role in evaluating various approaches to get through barriers that current physical theories impose. It is also argued that a search for barriers and limitations concerning feasibility in information processing and physical worlds are of equal or maybe even of larger importance than those to overcome the Church-Turing barrier and some communication barriers. It is also emphasized that relations between information processing in the real and virtual worlds, or between physical and information worlds, are likely very deep and more complex than realized. All that has even broader sense than usually realized because we are witnessing a radical shift in the main characterization of the current science in general. A shift from so called Galilean science dominated by mathematics, to the Informatics (based) science - an informatics methodology based science and technology.

[1]  Geoffrey C. Fox,et al.  Grid Computing: Making The Global Infrastructure a Reality: John Wiley & Sons , 2003 .

[2]  Jeffrey Bub,et al.  Characterizing Quantum Theory in Terms of Information-Theoretic Constraints , 2002 .

[3]  Ran Raz Quantum Information and the PCP Theorem , .

[4]  A. Zeilinger The message of the quantum , 2005, Nature.

[5]  J Barrett Information processing in non-signalling theories , 2005 .

[6]  José L. Balcázar,et al.  Structural Complexity I , 1988, EATCS Monographs on Theoretical Computer Science Series.

[7]  Nicolas Gisin,et al.  The Physics of No-Bit-Commitment: Generalized Quantum Non-Locality Versus Oblivious Transfer , 2005, Quantum Inf. Process..

[8]  Nicolas Gisin How come the Correlations , 2005 .

[9]  Tim Maudlin,et al.  The message of the quantum , 2006 .

[10]  Scott Aaronson Are Quantum States Exponentially Long Vectors , 2005 .

[11]  H. F. Chau,et al.  Why quantum bit commitment and ideal quantum coin tossing are impossible , 1997 .

[12]  Joel David Hamkins,et al.  Infinite Time Turing Machines With Only One Tape , 1999, Math. Log. Q..

[13]  Rolf Landauer,et al.  Information is Physical , 1991, Workshop on Physics and Computation.

[14]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.

[15]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  Ronald de Wolf,et al.  Private Quantum Channels and the Cost of Randomizing Quantum Information , 2000 .

[17]  István Németi,et al.  Relativistic computers and the Turing barrier , 2006, Appl. Math. Comput..

[18]  N J Cerf,et al.  Simulating maximal quantum entanglement without communication. , 2005, Physical review letters.

[19]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[20]  Hava T. Siegelmann,et al.  Neural networks and analog computation - beyond the Turing limit , 1999, Progress in theoretical computer science.

[21]  Scott Aaronson,et al.  Multilinear formulas and skepticism of quantum computing , 2003, STOC '04.

[22]  J ShortAnthony,et al.  The Physics of No-Bit-Commitment , 2006 .

[23]  B. Coecke Kindergarten Quantum Mechanics , 2005, quant-ph/0510032.

[24]  Scott Aaronson,et al.  Quantum computing, postselection, and probabilistic polynomial-time , 2004, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[25]  H. Buhrman,et al.  Limit on nonlocality in any world in which communication complexity is not trivial. , 2005, Physical review letters.

[26]  Nicolas Gisin,et al.  Can Relativity be Considered Complete? From Newtonian Nonlocality to Quantum Nonlocality and Beyond , 2005 .

[27]  Tien D Kieu Reply to ``The quantum algorithm of Kieu does not solve the Hilbert's tenth problem" , 2001 .

[28]  Yaoyun Shi,et al.  Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement , 2008, SIAM J. Comput..

[29]  B. Julsgaard,et al.  Experimental long-lived entanglement of two macroscopic objects , 2001, Nature.

[30]  István Németi,et al.  Non-Turing Computations Via Malament–Hogarth Space-Times , 2001 .

[31]  Wolfgang Tittel,et al.  The speed of quantum information and the preferred frame: analysis of experimental data , 2000, quant-ph/0007008.

[32]  S. Massar,et al.  Quantum entanglement can be simulated without communication , 2004, quant-ph/0410027.

[33]  R. Landauer Information is physical , 1991 .

[34]  Andris Ambainis,et al.  Dense quantum coding and a lower bound for 1-way quantum automata , 1998, STOC '99.

[35]  D. Kahn The codebreakers : the story of secret writing , 1968 .

[36]  A. Zeilinger,et al.  Matter-wave interferometer for large molecules. , 2002, Physical review letters.

[37]  Iordanis Kerenidis,et al.  Quantum multiparty communication complexity and circuit lower bounds , 2005, Mathematical Structures in Computer Science.

[38]  Avi Wigderson,et al.  P = BPP if E requires exponential circuits: derandomizing the XOR lemma , 1997, STOC '97.

[39]  K. Svozil The Church-Turing thesis as a guiding principle for physics , 1997, quant-ph/9710052.

[40]  Jan van Leeuwen,et al.  The Turing machine paradigm in contemporary computing , 2001 .

[41]  Tien D. Kieu,et al.  Quantum Algorithm for Hilbert's Tenth Problem , 2001, ArXiv.

[42]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[43]  Samson Abramsky,et al.  A categorical semantics of quantum protocols , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[44]  Francine Berman,et al.  Grid Computing: Making the Global Infrastructure a Reality , 2003 .

[45]  Scott Aaronson,et al.  NP-complete Problems and Physical Reality , 2005, Electron. Colloquium Comput. Complex..

[46]  Andrew Hodges,et al.  Can quantum computing solve classically unsolvable problems , 2005, quant-ph/0512248.

[47]  Dominic Mayers Unconditionally secure quantum bit commitment is impossible , 1997 .

[48]  Jozef Gruska Quantum Entanglement as a New Quantum Informational ProcessingResource , 2002 .

[49]  Jan van Leeuwen,et al.  Relativistic Computers and Non-uniform Complexity Theory , 2002, UMC.

[50]  M. Ozawa Universal uncertainty principle in the measurement operator formalism , 2005, quant-ph/0510083.

[51]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[52]  Valerio Scarani Feats, Features and Failures of the PR‐box , 2006 .

[53]  Jirí Wiedermann Globular Universe and Autopoietic Automata: A Framework for Artificial Life , 2005, ECAL.

[54]  Claudio Garola Truth and Completeness in Quantum Mechanics: A Semantic Viewpoint , 2005 .

[55]  Cristian S. Calude,et al.  Coins, Quantum Measurements, and Turing's Barrier , 2002, Quantum Inf. Process..

[56]  José L. Balcázar,et al.  Structural complexity 2 , 1990 .

[57]  Eyal Kushilevitz,et al.  Communication Complexity: Index of Notation , 1996 .

[58]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[59]  Eyal Kushilevitz,et al.  Communication Complexity , 1997, Adv. Comput..

[60]  S. Popescu,et al.  Causality and nonlocality as axioms for quantum mechanics , 1997, quant-ph/9709026.

[61]  H. J. Bernstein,et al.  Quantum Physics from A to Z , 2005, quant-ph/0505187.

[62]  John Watrous,et al.  Zero-knowledge against quantum attacks , 2005, STOC '06.

[63]  A. Winter,et al.  Implications of superstrong non-locality for cryptography , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[64]  D. Abrams,et al.  NONLINEAR QUANTUM MECHANICS IMPLIES POLYNOMIAL-TIME SOLUTION FOR NP-COMPLETE AND P PROBLEMS , 1998, quant-ph/9801041.

[65]  Scott Aaronson,et al.  Guest Column: NP-complete problems and physical reality , 2005, SIGA.

[66]  Joel David Hamkins,et al.  Infinite Time Turing Machines , 2000 .

[67]  R. Srikanth Computable Functions, the Church-Turing Thesis and the Quantum Measurement Problem , 2004 .

[68]  S. Massar,et al.  Nonlocal correlations as an information-theoretic resource , 2004, quant-ph/0404097.

[69]  B. S. Cirel'son Quantum generalizations of Bell's inequality , 1980 .

[70]  Gerard 't Hooft The mathematical basis for deterministic quantum mechanics , 2006 .

[71]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[72]  M. Hogarth Non-Turing Computers and Non-Turing Computability , 1994, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.