Pub Date : 2020-08-28DOI: 10.1142/s1230161220500079
V. Ignatyuk
We study the dynamical correlations in open quantum systems on an example of an exactly solvable dephasing model. The system of non-Markovian kinetic equations for the generalized coherence and qua...
{"title":"Dynamic Correlations in Open Quantum Systems: The Dephasing Model","authors":"V. Ignatyuk","doi":"10.1142/s1230161220500079","DOIUrl":"https://doi.org/10.1142/s1230161220500079","url":null,"abstract":"We study the dynamical correlations in open quantum systems on an example of an exactly solvable dephasing model. The system of non-Markovian kinetic equations for the generalized coherence and qua...","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"30 1","pages":"2050007:1-2050007:24"},"PeriodicalIF":0.8,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73941703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-28DOI: 10.1142/s1230161220500092
A. Türkmen, A. Verçin
Quantum error correction is studied in a framework consisting of an open quantum system and its environment, jointly subjected to a unitary action, and an interaction-free reference system. It has ...
{"title":"Quantum Error Correction in the Presence of Initial System-Environment Correlations","authors":"A. Türkmen, A. Verçin","doi":"10.1142/s1230161220500092","DOIUrl":"https://doi.org/10.1142/s1230161220500092","url":null,"abstract":"Quantum error correction is studied in a framework consisting of an open quantum system and its environment, jointly subjected to a unitary action, and an interaction-free reference system. It has ...","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"64 1","pages":"2050009:1-2050009:19"},"PeriodicalIF":0.8,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86132238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-11DOI: 10.1142/s1230161220500134
Jorge R. Bolanos-Serv'in, R. Quezada, Josué I. Rios-Cangas
We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator $Z$. By using these transition maps as Kraus (or noise) operators, an extension of the quantum energy transport model of 10.1142/S0219025718500182 describing the dynamics of an open quantum system of $N$-levels is presented. We deduce the structure of the invariant states which can be recovered by transporting states supported on the first level.
{"title":"Transition Maps between Hilbert Subspaces and Quantum Energy Transport","authors":"Jorge R. Bolanos-Serv'in, R. Quezada, Josué I. Rios-Cangas","doi":"10.1142/s1230161220500134","DOIUrl":"https://doi.org/10.1142/s1230161220500134","url":null,"abstract":"We use a natural generalization of the discrete Fourier transform to define transition maps between Hilbert subspaces and the global transport operator $Z$. By using these transition maps as Kraus (or noise) operators, an extension of the quantum energy transport model of 10.1142/S0219025718500182 describing the dynamics of an open quantum system of $N$-levels is presented. We deduce the structure of the invariant states which can be recovered by transporting states supported on the first level.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"52 1","pages":"2050013:1-2050013:22"},"PeriodicalIF":0.8,"publicationDate":"2020-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73626436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-13DOI: 10.1142/s1230161220500158
K. Grabowska, J. Grabowski, M. Kuś, G. Marmo
We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.
{"title":"Information geometry on groupoids: the case of singular metrics","authors":"K. Grabowska, J. Grabowski, M. Kuś, G. Marmo","doi":"10.1142/s1230161220500158","DOIUrl":"https://doi.org/10.1142/s1230161220500158","url":null,"abstract":"We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"116 1","pages":"2050015:1-2050015:19"},"PeriodicalIF":0.8,"publicationDate":"2020-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79274586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1142/s1230161220500067
F. Mukhamedov, Sondos M. Syam, S. Almazrouei
The present paper deals with a connection between quantum quadratic operators (QQOs) and quasi QQOs on 𝕄2(ℂ). We show that QQOs and quasi QQOs on 𝕄2(ℂ) coincide in the class of Volterra type of operators. To establish this result, we first describe these two kind of operators on the commutative part of 𝕄2(ℂ). Furthermore, in the last section, we introduce a quantum analogue of Volterra operators and provide concrete examples of such kind of operators. It is established that the considered examples also satisfy quasiness condition as well. The obtained results will allow to produce (with explicit conditions) a class of unital, but not trace-preserving positive maps of 𝕄2(ℂ).
{"title":"Few Remarks on Quasi Quantum Quadratic Operators on 필2(ℂ)","authors":"F. Mukhamedov, Sondos M. Syam, S. Almazrouei","doi":"10.1142/s1230161220500067","DOIUrl":"https://doi.org/10.1142/s1230161220500067","url":null,"abstract":"The present paper deals with a connection between quantum quadratic operators (QQOs) and quasi QQOs on 𝕄2(ℂ). We show that QQOs and quasi QQOs on 𝕄2(ℂ) coincide in the class of Volterra type of operators. To establish this result, we first describe these two kind of operators on the commutative part of 𝕄2(ℂ). Furthermore, in the last section, we introduce a quantum analogue of Volterra operators and provide concrete examples of such kind of operators. It is established that the considered examples also satisfy quasiness condition as well. The obtained results will allow to produce (with explicit conditions) a class of unital, but not trace-preserving positive maps of 𝕄2(ℂ).","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"142 2 1","pages":"2050006:1-2050006:20"},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80982088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1142/s1230161220800013
K. Życzkowski
{"title":"Book Review: Principles of Quantum Computation and Information","authors":"K. Życzkowski","doi":"10.1142/s1230161220800013","DOIUrl":"https://doi.org/10.1142/s1230161220800013","url":null,"abstract":"","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"46 1","pages":"2080001:1-2080001:2"},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74273134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1142/s1230161220500080
Zahra Eslami Giski
The aim of this study is to extend the results concerning the Shannon entropy and Kullback–Leibler divergence in sequential effect algebra to the case of Rényi entropy and Rényi divergence. For this purpose, the Rényi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Rényi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback–Leibler divergence and Shannon’s entropy of partitions in a given sequential effect algebra can be obtained as limits of their Rényi divergence and Rényi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.
{"title":"Rényi Entropy and Rényi Divergence in Sequential Effect Algebra","authors":"Zahra Eslami Giski","doi":"10.1142/s1230161220500080","DOIUrl":"https://doi.org/10.1142/s1230161220500080","url":null,"abstract":"The aim of this study is to extend the results concerning the Shannon entropy and Kullback–Leibler divergence in sequential effect algebra to the case of Rényi entropy and Rényi divergence. For this purpose, the Rényi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Rényi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback–Leibler divergence and Shannon’s entropy of partitions in a given sequential effect algebra can be obtained as limits of their Rényi divergence and Rényi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"26 1","pages":"2050008:1-2050008:30"},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75333341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-05DOI: 10.1142/s1230161220500055
Khadija Bessadok, F. Fagnola, Skander Hachicha
We study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space Lq,α2....
{"title":"Classical and Quantum Markov Processes Associated with q-Bessel Operators","authors":"Khadija Bessadok, F. Fagnola, Skander Hachicha","doi":"10.1142/s1230161220500055","DOIUrl":"https://doi.org/10.1142/s1230161220500055","url":null,"abstract":"We study the fundamental properties of classical and quantum Markov processes generated by q-Bessel operators and their extension to the algebra of all bounded operators on the Hilbert space Lq,α2....","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"2 1","pages":"2050005:1-2050005:16"},"PeriodicalIF":0.8,"publicationDate":"2020-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90049357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-04DOI: 10.1142/s1230161220500122
Ryota Kyokawa, H. Moriya, H. Tamura
We consider an open Dicke model made of a single infinite-component vector spin and a single-mode harmonic oscillator assuming a Jaynes-Cummings type interaction between them. We study its algebraic structure and dynamics based on superoperator formalism. It is shown that by an explicit invertible superoperator its Liouvillian is transformed into a sum of two independent Liouvillians that are generated by a dressed spin and a dressed harmonic oscillator, respectively.
{"title":"On the Open Dicke-Type Model Generated by an Infinite-Component Vector Spin","authors":"Ryota Kyokawa, H. Moriya, H. Tamura","doi":"10.1142/s1230161220500122","DOIUrl":"https://doi.org/10.1142/s1230161220500122","url":null,"abstract":"We consider an open Dicke model made of a single infinite-component vector spin and a single-mode harmonic oscillator assuming a Jaynes-Cummings type interaction between them. We study its algebraic structure and dynamics based on superoperator formalism. It is shown that by an explicit invertible superoperator its Liouvillian is transformed into a sum of two independent Liouvillians that are generated by a dressed spin and a dressed harmonic oscillator, respectively.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"21 1","pages":"2050012:1-2050012:25"},"PeriodicalIF":0.8,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73563773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-26DOI: 10.1142/S1230161220500195
Shrikant Utagi, V. Rao, R. Srikanth, Subhashis Banerjee
We study a class of qubit non-Markovian general Pauli dynamical maps with multiple singularities in the generator. We discuss a few easy examples involving trigonometric or other nonmonotonic time dependence of the map, and discuss in detail the structure of channels which don’t have any trigonometric functional dependence. We demystify the concept of a singularity here, showing that it corresponds to a point where the dynamics can be regular but the map is momentarily noninvertible, and this gives a basic guideline to construct such non-invertible non-Markovian channels. Most members of the channels in the considered family are quasi-eternally non-Markovian (QENM), which is a broader class of non-Markovian channels than the eternal non-Markovian channels. Specifically, the measure of quasi-eternal non-Markovian (QENM) channels in the considered class is shown to be [Formula: see text] in the isotropic case, and about 0.96 in the anisotropic case.
{"title":"A Class of Quasi-Eternal Non-Markovian Pauli Channels and Their Measure","authors":"Shrikant Utagi, V. Rao, R. Srikanth, Subhashis Banerjee","doi":"10.1142/S1230161220500195","DOIUrl":"https://doi.org/10.1142/S1230161220500195","url":null,"abstract":"We study a class of qubit non-Markovian general Pauli dynamical maps with multiple singularities in the generator. We discuss a few easy examples involving trigonometric or other nonmonotonic time dependence of the map, and discuss in detail the structure of channels which don’t have any trigonometric functional dependence. We demystify the concept of a singularity here, showing that it corresponds to a point where the dynamics can be regular but the map is momentarily noninvertible, and this gives a basic guideline to construct such non-invertible non-Markovian channels. Most members of the channels in the considered family are quasi-eternally non-Markovian (QENM), which is a broader class of non-Markovian channels than the eternal non-Markovian channels. Specifically, the measure of quasi-eternal non-Markovian (QENM) channels in the considered class is shown to be [Formula: see text] in the isotropic case, and about 0.96 in the anisotropic case.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"13 1","pages":"2050019:1-2050019:20"},"PeriodicalIF":0.8,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82158605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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