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Quantum Kolmogorov complexity based on classical descriptions

P.M.B. Vitanyi
<span title="">2001</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
Quantum Kolmogorov complexity coincides with the classical Kolmogorov complexity on the classical domain.  ...  This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions.  ...  We propose a theory of quantum Kolmogorov complexity based on classical descriptions and derive the results given in the abstract. A preliminary partial version appeared as [19] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/18.945258">doi:10.1109/18.945258</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/opbizz2wt5atrak6wqw4yi26sq">fatcat:opbizz2wt5atrak6wqw4yi26sq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706122216/https://www.cwi.nl/~paulv/papers/quantumkolmcompl.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/eb/e9/ebe93471cc7a9f16e1d20049d98096b306ff7394.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/18.945258"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Second Quantized Kolmogorov Complexity [article]

Caroline Rogers, Vlatko Vedral, Rajagopal Nagarajan
<span title="2008-09-16">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The Kolmogorov complexity of a string is the length of its shortest description.  ...  We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties.  ...  Quantum Kolmogorov Complexity based on Classical Descriptions Vitanyi [32] defined a prefix quantum Kolmogorov complexity based on classical descriptions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0809.2642v1">arXiv:0809.2642v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7cjorrvo3nbp3kvqfqtyx3y7zu">fatcat:7cjorrvo3nbp3kvqfqtyx3y7zu</a> </span>
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Fuzzy Kolmogorov Complexity Based on a Classical Description

Songsong Dai
<span title="2020-01-04">2020</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
The classical Kolmogorov complexity is extended to the fuzzy domain retaining classical descriptions.  ...  We define the fuzzy Kolmogorov complexity as the minimum classical description length of a finite-valued fuzzy language through a universal finite-valued fuzzy Turing machine that produces the desired  ...  This corollary is the property of classical Kolmogorov complexity in [6] . Upper Bound on Complexity In the classical case, we have the following upper bound of classical Kolmogorov complexity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e22010066">doi:10.3390/e22010066</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/33285841">pmid:33285841</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5bsdkboymzc5tgdechpxb3lzme">fatcat:5bsdkboymzc5tgdechpxb3lzme</a> </span>
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Three Approaches to the Quantitative Definition of Information in an Individual Pure Quantum State

Paul Vitanyi
<span title="2000-05-04">2000</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity.  ...  Classical Kolmogorov complexity coincides with the new quantum Kolmogorov complexity restricted to the classical domain.  ...  I thank Harry Buhrman, Richard Cleve, Wim van Dam, Barbara Terhal, John Tromp, and Ronald de Wolf for discussions and comments on QKC.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9907035v3">arXiv:quant-ph/9907035v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5bodf4zt7vau5f5atcxhns64ci">fatcat:5bodf4zt7vau5f5atcxhns64ci</a> </span>
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Quantum Kolmogorov complexity and bounded quantum memory

Takayuki Miyadera
<span title="2011-04-14">2011</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
We employed a toy two-party protocol in which Bob by using a bounded quantum memory and an unbounded classical memory estimates a message that was encoded in qubits by Alice in one of the bases X or Z.  ...  In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information.  ...  QUANTUM KOLMOGOROV COMPLEXITY BASED ON CLASSICAL DESCRIPTION The classical Kolmogorov complexity of a binary sequence is defined by the length of the shortest program, as proposed by Kolmogorov [6] and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.83.042316">doi:10.1103/physreva.83.042316</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lgmwrsvaxzgzhpp6v56i6i7dmq">fatcat:lgmwrsvaxzgzhpp6v56i6i7dmq</a> </span>
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The Second Quantized Quantum Turing Machine and Kolmogorov Complexity [article]

Caroline Rogers, Vlatko Vedral
<span title="2008-04-05">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give examples where second quantized and quantum Kolmogorov complexity differ.  ...  We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity.  ...  Vitanyi [5] also provided a definition of quantum Kolmogorov complexity based on classical descriptions, where a penalty factor was added depending on the accuracy of the classical description.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/0506266v2">arXiv:quant-ph/0506266v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dndj7fyopvhepm3hobd3fqar5q">fatcat:dndj7fyopvhepm3hobd3fqar5q</a> </span>
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THE SECOND QUANTIZED QUANTUM TURING MACHINE AND KOLMOGOROV COMPLEXITY

CAROLINE ROGERS, VLATKO VEDRAL
<span title="2008-05-20">2008</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rirs4jk2nrd53f4npjx2zfedbu" style="color: black;">Modern physics letters B</a> </i> &nbsp;
We give examples where second quantized and quantum Kolmogorov complexity differ.  ...  We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity.  ...  Vitanyi [5] also provided a definition of quantum Kolmogorov complexity based on classical descriptions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s021798490801464x">doi:10.1142/s021798490801464x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3q3sy6p5wjh3fodi3kiddyrfpa">fatcat:3q3sy6p5wjh3fodi3kiddyrfpa</a> </span>
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On the Quantum Kolmogorov Complexity of Classical Strings [article]

Markus Mueller
<span title="2009-06-09">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant.  ...  We outline a mathematical proof of this statement, based on an inequality for outputs of quantum operations and a classical program for the simulation of a universal quantum computer.  ...  This is called the "base length" by Boström and Felbinger in Ref. 10 . Quantum Kolmogorov complexity shares many properties with its classical counterpart.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0707.2924v2">arXiv:0707.2924v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n7xfqq7xmzgxjeyke4yt2snukm">fatcat:n7xfqq7xmzgxjeyke4yt2snukm</a> </span>
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QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS

CATERINA E. MORA, HANS J. BRIEGEL, BARBARA KRAUS
<span title="">2007</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ozpwqwobnbh3jcc4pclha67lny" style="color: black;">International Journal of Quantum Information</a> </i> &nbsp;
This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity.  ...  We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially  ...  In [14] , on the contrary, the author proposes a definition of quantum Kolmogorov complexity based on the classical description of the state.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0219749907003171">doi:10.1142/s0219749907003171</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/27eptxbcxbblxh7kuybxeffyte">fatcat:27eptxbcxbblxh7kuybxeffyte</a> </span>
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Quantum Kolmogorov complexity and its applications [article]

C. Mora, H. Briegel, B. Kraus
<span title="2006-10-13">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity.  ...  We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially  ...  In [14] , on the contrary, the author proposes a definition of quantum Kolmogorov complexity based on the classical description of the state.  ... 
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Quantum Kolmogorov Complexity and Information-Disturbance Theorem

Takayuki Miyadera
<span title="2011-03-29">2011</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
In this paper, a representation of the information-disturbance theorem based on the quantum Kolmogorov complexity that was defined by P. Vitanyi has been examined.  ...  The problem was formulated in a cryptographic setting and quantitative relationships between complexities have been derived.  ...  Quantum Kolmogorov Complexity Based on Classical Description Recently some quantum versions of Kolmogorov complexity were proposed by a several researchers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e13040778">doi:10.3390/e13040778</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xaryz7p2ibd3xa7snmc7dus5ba">fatcat:xaryz7p2ibd3xa7snmc7dus5ba</a> </span>
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Page 2286 of Mathematical Reviews Vol. , Issue 2003C [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(NL-MATH; Amsterdam) Quantum Kolmogorov complexity based on classical descriptions. (English summary) IEEE Trans. Inform.  ...  (NL-MATH; Amsterdam) Correction to: “Quantum Kolmogorov complexity based on classical descriptions”. IEEE Trans. Inform. Theory 48 (2002), no. 4, 1000.  ... 
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No "No-Go" [article]

Andrei Khrennikov
<span title="2003-08-29">2003</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Einstein who was sure that QM is not complete and a finer description is possible.  ...  Thus in spite of all "No-Go" theorems (e.g., von Neumann, Kochen and Specker,..., Bell) we found a realist basis of quantum mechanics. I think that our model would totally satisfy A.  ...  Our derivation of interference of probabilities is based only on one postulate: Contextuality of probabilities: Probabilities depend on complexes of physical conditions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/0308166v1">arXiv:quant-ph/0308166v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mrcpjulflfbdxnbchwfkoohpkq">fatcat:mrcpjulflfbdxnbchwfkoohpkq</a> </span>
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Quantum Kolmogorov complexity and quantum key distribution

Takayuki Miyadera, Hideki Imai
<span title="2009-01-26">2009</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov complexity that was recently defined by Vit\'anyi.  ...  The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory.  ...  QUANTUM KOLMOGOROV COMPLEXITY BASED ON CLASSICAL DESCRIPTION Recently some quantum versions of Kolmogorov complexity were proposed by a several researchers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.79.012324">doi:10.1103/physreva.79.012324</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iiqm533gl5c2ncc5ve3i7jtnby">fatcat:iiqm533gl5c2ncc5ve3i7jtnby</a> </span>
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Classical and quantum randomness and the financial market [article]

Andrei Khrennikov
<span title="2007-04-22">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However, our hypothesis on "quantumness" of financial data should be tested experimentally (as opposed to the conventional description based on the noncontextual classical probabilistic approach).  ...  Our analysis implies that it might be that a quantum-like probabilistic description is more natural for financial market than the classical one.  ...  Such a description (which is based on the classical probability theory and its application to the financial market -the network approach) generates classical financial processes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0704.2865v1">arXiv:0704.2865v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h4sha7hrzrfnfdiiwbq3brcukq">fatcat:h4sha7hrzrfnfdiiwbq3brcukq</a> </span>
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