{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T18:07:02Z","timestamp":1694628422106},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2006,12,8]],"date-time":"2006-12-08T00:00:00Z","timestamp":1165536000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2006,12,8]],"date-time":"2006-12-08T00:00:00Z","timestamp":1165536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Comput"],"published-print":{"date-parts":[[2007,6]]},"DOI":"10.1007\/s11047-006-9017-5","type":"journal-article","created":{"date-parts":[[2006,12,7]],"date-time":"2006-12-07T11:07:09Z","timestamp":1165489629000},"page":"133-150","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Entropy and algorithmic complexity in quantum information theory"],"prefix":"10.1007","volume":"6","author":[{"given":"Fabio","family":"Benatti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2006,12,8]]},"reference":[{"key":"9017_CR1","doi-asserted-by":"publisher","first-page":"1524","DOI":"10.1137\/S0097539795293639","volume":"26","author":"LM Adleman","year":"1997","unstructured":"Adleman LM, Demarrais J, Huang MA (1997) Quantum computability. SIAM Journal on Computing 26:1524\u20131540","journal-title":"SIAM Journal on Computing"},{"key":"9017_CR23","doi-asserted-by":"crossref","unstructured":"Alicki R and Fannes M (2001) Quantum Dynamical Systems. Oxford University Press","DOI":"10.1093\/acprof:oso\/9780198504009.001.0001"},{"key":"9017_CR3","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/BF00749625","volume":"33","author":"R Alicki","year":"1995","unstructured":"Alicki R, Narnhofer H (1995). Comparison of dynamical entropies for the noncommutative shifts. Letters in Mathematical Physics 33:241\u2013247","journal-title":"Letters in Mathematical Physics"},{"key":"9017_CR2","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0370-1573(81)90186-1","volume":"75","author":"VM Alekseev","year":"1981","unstructured":"Alekseev VM, Yakobson MV (1981) Symbolic dynamics and hyperbolic dynamic systems. Physics Reports 75:287","journal-title":"Physics Reports"},{"key":"9017_CR14","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s00220-006-0027-z","volume":"265","author":"F Benatti","year":"2006","unstructured":"Benatti F, Krueger T, Mueller M, Siegmund-Schultze R and Szko\u0142a A (2006) Entropy and Algorithmic Complexity in Quantum Information Theory: A Quantum Brudno\u2019s Theorem. Commun. Math. Phys. 265: 437\u2013461","journal-title":"Commun. Math. Phys."},{"key":"9017_CR4","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1137\/S0097539796300921","volume":"26","author":"E Bernstein","year":"1997","unstructured":"Bernstein E, Vazirani U (1997) Quantum complexity theory. SIAM Journal on Computing 26:1411\u20131473","journal-title":"SIAM Journal on Computing"},{"key":"9017_CR5","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1006\/jcss.2001.1765","volume":"63","author":"A Berthiaume","year":"2001","unstructured":"Berthiaume A, Van Dam W, Laplante S (2001). Quantum Kolmogorov complexity. Journal of Computer and System Sciences 63:201\u2013221","journal-title":"Journal of Computer and System Sciences"},{"key":"9017_CR6","unstructured":"Billingsley P (1965) Ergodic Theory and Information. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York"},{"key":"9017_CR17","unstructured":"Bjelakovi\u0107 I, Kr\u00fcger T, Siegmund-Schultze Ra and Szko \u0142a A (2003) Chained Typical Subspaces-a Quantum Version of Breiman\u2019s Theorem, quant-ph\/0301177"},{"key":"9017_CR7","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s00222-003-0318-3","volume":"155","author":"I Bjelakovi\u0107","year":"2004","unstructured":"Bjelakovi\u0107 I, Kr\u00fcger T, Siegmund-Schultze Ra, Szko\u0142a A (2004). The Shannon\u2013McMillan theorem for ergodic quantum lattice systems. Inventiones Mathematicae 155:203\u2013222","journal-title":"Inventiones Mathematicae"},{"key":"9017_CR8","first-page":"127","volume":"2","author":"AA Brudno","year":"1983","unstructured":"Brudno AA (1983). Entropy and the complexity of the trajectories of a dynamical system. Transactions of the Moscow Mathematical Society 2:127\u2013151","journal-title":"Transactions of the Moscow Mathematical Society"},{"key":"9017_CR11","unstructured":"Calude C (2002) Information and Randomness. An Algorithmic Perspective, 2nd edn. Springer-Verlag, Berlin"},{"key":"9017_CR12","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1145\/321356.321363","volume":"13","author":"GJ Chaitin","year":"1966","unstructured":"Chaitin GJ (1966). On the length of programs for computing binary sequences. Journal of the Association for Computing Machinery 13:547\u2013569","journal-title":"Journal of the Association for Computing Machinery"},{"key":"9017_CR13","doi-asserted-by":"crossref","unstructured":"Cover TM and Thomas JA (1991) Elements of Information Theory, Wiley Series in Telecommunications. John Wiley & Sons, New York","DOI":"10.1002\/0471200611"},{"key":"9017_CR15","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1093\/bjps\/55.3.411","volume":"55","author":"R Frigg","year":"2004","unstructured":"Frigg R (2004). In what sense is the Kolmogorov\u2013Sinai entropy a measure for chaotic behaviour? Bridging the gap between dynamical systems theory and communication theory. British Journal for the Philosophy of Science 55:411\u2013434","journal-title":"British Journal for the Philosophy of Science"},{"key":"9017_CR16","doi-asserted-by":"publisher","first-page":"6859","DOI":"10.1088\/0305-4470\/34\/35\/312","volume":"34","author":"P G\u00e1cs","year":"2001","unstructured":"G\u00e1cs P (2001) Quantum algorithmic entropy. Journal of Physics A: Mathematical and General 34:6859\u20136880","journal-title":"Journal of Physics A: Mathematical and General"},{"issue":"4","key":"9017_CR18","doi-asserted-by":"crossref","first-page":"359","DOI":"10.26421\/QIC3.4-5","volume":"3","author":"A Kaltchenko","year":"2003","unstructured":"Kaltchenko A., Yang E.H. (2003). Universal compression of ergodic quantum sources. Quantum Information and Computation 3(4):359\u2013375","journal-title":"Quantum Information and Computation"},{"key":"9017_CR19","first-page":"4","volume":"1","author":"AN Kolmogorov","year":"1965","unstructured":"Kolmogorov AN (1965) Three approaches to the quantitative definition on information. Problems of Information Transmission 1:4\u20137","journal-title":"Problems of Information Transmission"},{"key":"9017_CR20","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1109\/TIT.1968.1054210","volume":"14","author":"AN Kolmogorov","year":"1968","unstructured":"Kolmogorov AN (1968). Logical basis for information theory and probability theory. IEEE Transactions on Information Theory 14:662\u2013664","journal-title":"IEEE Transactions on Information Theory"},{"key":"9017_CR21","doi-asserted-by":"crossref","unstructured":"Li M and Vitanyi P (1997) An introduction to Kolmogorov complexity and its applications. Springer Verlag","DOI":"10.1007\/978-1-4757-2606-0"},{"key":"9017_CR10","doi-asserted-by":"crossref","first-page":"200503","DOI":"10.1103\/PhysRevLett.95.200503","volume":"95","author":"C Mora","year":"2005","unstructured":"Mora C and Briegel HJ (2005) Algorithmic complexity and entanglement of quantum states. Phys. Rev. Lett. 95:200503","journal-title":"Phys. Rev. Lett."},{"key":"9017_CR22","volume-title":"Quantum computation and quantum information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge"},{"key":"9017_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0019-9958(64)90223-2","volume":"7","author":"RJ Solomonoff","year":"1964","unstructured":"Solomonoff RJ (1964) A formal theory of inductive inference. Information and Control 7, 1\u201322, 224\u2013254","journal-title":"Information and Control"},{"key":"9017_CR25","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/0375-9601(90)90408-G","volume":"143","author":"K Svozil","year":"1990","unstructured":"Svozil K (1990) The quantum coin toss-testing microphysical undecidability. Physics Letters A 143:433\u2013437","journal-title":"Physics Letters A"},{"issue":"1","key":"9017_CR26","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1070\/RM1990v045n01ABEH002321","volume":"45","author":"VA Uspenskii","year":"1990","unstructured":"Uspenskii VA, Semenov AL, Shen AKh (1990) Can an individual sequence of zeros and ones be random. Uspekhi Mat. Nauk. 45(1):105\u2013162","journal-title":"Russian Math. Survey"},{"issue":"6","key":"9017_CR27","doi-asserted-by":"publisher","first-page":"2464","DOI":"10.1109\/18.945258","volume":"47","author":"P Vit\u00e1nyi","year":"2001","unstructured":"Vit\u00e1nyi P (2001) Quantum Kolmogorov complexity based on classical descriptions. IEEE Transactions on Information Theory 47(6):2464\u20132479","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Natural Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-006-9017-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11047-006-9017-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-006-9017-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11047-006-9017-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T22:40:36Z","timestamp":1652827236000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11047-006-9017-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12,8]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["9017"],"URL":"https:\/\/doi.org\/10.1007\/s11047-006-9017-5","relation":{},"ISSN":["1567-7818","1572-9796"],"issn-type":[{"value":"1567-7818","type":"print"},{"value":"1572-9796","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12,8]]},"assertion":[{"value":"1 November 2005","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2006","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 April 2006","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 December 2006","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}