Pub Date : 2022-02-11DOI: 10.1142/S1230161223500014
Markus Hasenöhrl, Matthias C. Caro
The problem of characterizing GKLS-generators and CP-maps with an invariant von Neumann algebra [Formula: see text] appeared in different guises in the literature. We prove two unifying results, which hold even for weakly closed *-algebras: first, we show how to construct a normal form for [Formula: see text]-invariant GKLS-generators, if a normal form for [Formula: see text]-invariant CP-maps is known — rendering the two problems essentially equivalent. Second, we provide a normal form for [Formula: see text]-invariant CP-maps if [Formula: see text] is atomic (which includes the finite-dimensional case). As an application we reproduce several results from the literature as direct consequences of our characterizations and thereby point out connections between different fields.
用不变的冯·诺伊曼代数(公式:见文本)表征gkls -生成器和cp -映射的问题以不同的形式出现在文献中。我们证明了两个统一的结果，它们甚至对弱闭*-代数也成立:首先，我们展示了如何构造[公式:见文]不变gkls生成器的范式，如果[公式:见文]不变cp -映射的范式已知，则使两个问题本质上等价。其次，如果[Formula: see text]是原子的(包括有限维的情况)，我们为[Formula: see text]提供了一种标准形式-不变cp -映射。作为一种应用，我们从文献中复制了几个结果，作为我们描述的直接结果，从而指出了不同领域之间的联系。
{"title":"On the Generators of Quantum Dynamical Semigroups with Invariant Subalgebras","authors":"Markus Hasenöhrl, Matthias C. Caro","doi":"10.1142/S1230161223500014","DOIUrl":"https://doi.org/10.1142/S1230161223500014","url":null,"abstract":"The problem of characterizing GKLS-generators and CP-maps with an invariant von Neumann algebra [Formula: see text] appeared in different guises in the literature. We prove two unifying results, which hold even for weakly closed *-algebras: first, we show how to construct a normal form for [Formula: see text]-invariant GKLS-generators, if a normal form for [Formula: see text]-invariant CP-maps is known — rendering the two problems essentially equivalent. Second, we provide a normal form for [Formula: see text]-invariant CP-maps if [Formula: see text] is atomic (which includes the finite-dimensional case). As an application we reproduce several results from the literature as direct consequences of our characterizations and thereby point out connections between different fields.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"13 1","pages":"2350001:1-2350001:24"},"PeriodicalIF":0.8,"publicationDate":"2022-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80644542","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 : 2022-01-29DOI: 10.1142/S1230161222500020
Koorosh Sadri, F. Shahbeigi, Z. Puchała, K. Życzkowski
We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group [Formula: see text] plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set [Formula: see text] of accessible maps we show that this set is nonconvex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set [Formula: see text] covers a positive volume in the polytope of all convex combinations of the elements of the group.
{"title":"Accessible Maps in a Group of Classical or Quantum Channels","authors":"Koorosh Sadri, F. Shahbeigi, Z. Puchała, K. Życzkowski","doi":"10.1142/S1230161222500020","DOIUrl":"https://doi.org/10.1142/S1230161222500020","url":null,"abstract":"We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group [Formula: see text] plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set [Formula: see text] of accessible maps we show that this set is nonconvex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set [Formula: see text] covers a positive volume in the polytope of all convex combinations of the elements of the group.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"33 1","pages":"2250002:1-2250002:40"},"PeriodicalIF":0.8,"publicationDate":"2022-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73394779","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 : 2022-01-14DOI: 10.1142/S1230161222500044
Federico Roccati, G. Palma, F. Ciccarello, F. Bagarello
A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.
{"title":"Non-Hermitian Physics and Master Equations","authors":"Federico Roccati, G. Palma, F. Ciccarello, F. Bagarello","doi":"10.1142/S1230161222500044","DOIUrl":"https://doi.org/10.1142/S1230161222500044","url":null,"abstract":"A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"53 1","pages":"2250004:1-2250004:20"},"PeriodicalIF":0.8,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90536926","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 : 2022-01-01DOI: 10.1007/978-3-030-96745-1
T. Dittrich
{"title":"Information Dynamics: In Classical and Quantum Systems","authors":"T. Dittrich","doi":"10.1007/978-3-030-96745-1","DOIUrl":"https://doi.org/10.1007/978-3-030-96745-1","url":null,"abstract":"","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79135080","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 : 2021-12-01DOI: 10.1142/s1230161221500177
K. Życzkowski
Some achievements of the late Andrzej Kossakowski in the field of statistical physics and quantum theory are presented. We recall also his attempt to find an analytical solution of the 3-dimensional Ising model.
{"title":"Three Favourite Dimensions of Andrzej: Along His Path to a Scientific Discovery","authors":"K. Życzkowski","doi":"10.1142/s1230161221500177","DOIUrl":"https://doi.org/10.1142/s1230161221500177","url":null,"abstract":"Some achievements of the late Andrzej Kossakowski in the field of statistical physics and quantum theory are presented. We recall also his attempt to find an analytical solution of the 3-dimensional Ising model.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"13 1","pages":"2150017:1-2150017:6"},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88532193","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 : 2021-12-01DOI: 10.1142/S1230161221500207
Matteo Piccolini, Farzam Nosrati, R. Morandotti, R. Franco
We extend a procedure exploiting spatial indistinguishability of identical particles to recover the spoiled entanglement between two qubits interacting with Markovian noisy environments. Here, the spatially localized operations and classical communication (sLOCC) operational framework is used to activate the entanglement restoration from the indistinguishable constituents. We consider the realistic scenario where noise acts for the whole duration of the process. Three standard types of noises are considered: a phase damping, a depolarizing, and an amplitude damping channel. Within this general scenario, we find the entanglement to be restored in an amount proportional to the degree of spatial indistinguishability. These results elevate sLOCC to a practical framework for accessing and utilizing quantum state protection within a quantum network of spatially indistinguishable subsystems.
{"title":"Indistinguishability-Enhanced Entanglement Recovery by Spatially Localized Operations and Classical Communication","authors":"Matteo Piccolini, Farzam Nosrati, R. Morandotti, R. Franco","doi":"10.1142/S1230161221500207","DOIUrl":"https://doi.org/10.1142/S1230161221500207","url":null,"abstract":"We extend a procedure exploiting spatial indistinguishability of identical particles to recover the spoiled entanglement between two qubits interacting with Markovian noisy environments. Here, the spatially localized operations and classical communication (sLOCC) operational framework is used to activate the entanglement restoration from the indistinguishable constituents. We consider the realistic scenario where noise acts for the whole duration of the process. Three standard types of noises are considered: a phase damping, a depolarizing, and an amplitude damping channel. Within this general scenario, we find the entanglement to be restored in an amount proportional to the degree of spatial indistinguishability. These results elevate sLOCC to a practical framework for accessing and utilizing quantum state protection within a quantum network of spatially indistinguishable subsystems.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"2 1","pages":"2150020:1-2150020:28"},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82010715","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 : 2021-12-01DOI: 10.1142/s1230161221500153
D. Chruściński
I review here a small part of Andrzej Kossakowski scientific activity focusing on his pioneering contribution to the evolution of open quantum systems (celebrated Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation) and positive maps in operator algebras. These particular topics turned out to be of primary importance for fundamentals of quantum physics and the rapid development of modern quantum information theory.
{"title":"The Legacy of Andrzej Kossakowski","authors":"D. Chruściński","doi":"10.1142/s1230161221500153","DOIUrl":"https://doi.org/10.1142/s1230161221500153","url":null,"abstract":"I review here a small part of Andrzej Kossakowski scientific activity focusing on his pioneering contribution to the evolution of open quantum systems (celebrated Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation) and positive maps in operator algebras. These particular topics turned out to be of primary importance for fundamentals of quantum physics and the rapid development of modern quantum information theory.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"77 1","pages":"2150015:1-2150015:19"},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84961167","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 : 2021-12-01DOI: 10.1142/s1230161221500165
S. Pascazio
When someone disappears, where do their ideas go?
当一个人消失时，他们的想法去了哪里?
{"title":"Remembering Andrzej Kossakowski","authors":"S. Pascazio","doi":"10.1142/s1230161221500165","DOIUrl":"https://doi.org/10.1142/s1230161221500165","url":null,"abstract":"When someone disappears, where do their ideas go?","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"12 1","pages":"2150016:1-2150016:6"},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88311272","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 : 2021-12-01DOI: 10.1142/s1230161221500189
L. Accardi, Y. Lu, A. Souissi
We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.
{"title":"A Markov-Dobrushin Inequality for Quantum Channels","authors":"L. Accardi, Y. Lu, A. Souissi","doi":"10.1142/s1230161221500189","DOIUrl":"https://doi.org/10.1142/s1230161221500189","url":null,"abstract":"We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"53 1","pages":"2150018:1-2150018:18"},"PeriodicalIF":0.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86137224","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 : 2021-09-22DOI: 10.1142/S1230161222500172
L. Accardi, Tarek Hamdi, Y. Lu
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonically associated to the standard semi-circle random variable [Formula: see text], characterized by the fact that its probability distribution is the semi-circle law [Formula: see text] on [Formula: see text]. We prove that, in the identification of [Formula: see text] with the [Formula: see text]-mode interacting Fock space [Formula: see text], defined by the orthogonal polynomial gradation of [Formula: see text], [Formula: see text] is mapped into position operator and its canonically associated momentum operator [Formula: see text] into [Formula: see text] times the [Formula: see text]-Hilbert transform [Formula: see text] on [Formula: see text]. In the first part of the present paper, after briefly describing the simpler case of the [Formula: see text]-harmonic oscillator, we find an explicit expression for the action, on the [Formula: see text]-orthogonal polynomials, of the semi-circle analogue of the translation group [Formula: see text] and of the semi-circle analogue of the free evolution [Formula: see text], respectively, in terms of Bessel functions of the first kind and of confluent hyper-geometric series. These results require the solution of the inverse normal order problem on the quantum algebra canonically associated to the classical semi-circle random variable and are derived in the second part of the present paper. Since the problem to determine, with purely analytic techniques, the explicit form of the action of [Formula: see text] and [Formula: see text] on the [Formula: see text]-orthogonal polynomials is difficult, the above mentioned results show the power of the combination of these techniques with those developed within the algebraic approach to the theory of orthogonal polynomials.
{"title":"The Quantum Mechanics Canonically Associated to Free Probability I: Free Momentum and Associated Kinetic Energy","authors":"L. Accardi, Tarek Hamdi, Y. Lu","doi":"10.1142/S1230161222500172","DOIUrl":"https://doi.org/10.1142/S1230161222500172","url":null,"abstract":"After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonically associated to the standard semi-circle random variable [Formula: see text], characterized by the fact that its probability distribution is the semi-circle law [Formula: see text] on [Formula: see text]. We prove that, in the identification of [Formula: see text] with the [Formula: see text]-mode interacting Fock space [Formula: see text], defined by the orthogonal polynomial gradation of [Formula: see text], [Formula: see text] is mapped into position operator and its canonically associated momentum operator [Formula: see text] into [Formula: see text] times the [Formula: see text]-Hilbert transform [Formula: see text] on [Formula: see text]. In the first part of the present paper, after briefly describing the simpler case of the [Formula: see text]-harmonic oscillator, we find an explicit expression for the action, on the [Formula: see text]-orthogonal polynomials, of the semi-circle analogue of the translation group [Formula: see text] and of the semi-circle analogue of the free evolution [Formula: see text], respectively, in terms of Bessel functions of the first kind and of confluent hyper-geometric series. These results require the solution of the inverse normal order problem on the quantum algebra canonically associated to the classical semi-circle random variable and are derived in the second part of the present paper. Since the problem to determine, with purely analytic techniques, the explicit form of the action of [Formula: see text] and [Formula: see text] on the [Formula: see text]-orthogonal polynomials is difficult, the above mentioned results show the power of the combination of these techniques with those developed within the algebraic approach to the theory of orthogonal polynomials.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"20 1","pages":"2250017:1-2250017:31"},"PeriodicalIF":0.8,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87105283","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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