Pub Date : 2021-09-01DOI: 10.1142/s1230161221500116
I. Lyris, P. Lykourgias, A. I. Karanikas
In this work we study the reduced dynamics of a system embedded in a quantum environment, with the use of correlation functions produced through appropriately defined reduced generating functionals. Our construction is based on expressing these functionals in terms of consistently defined coherent-state path integrals in the framework of the Keldysh-Schwinger out-of-equilibrium formalism.
{"title":"Reduced Dynamics in Open Bosonic and Fermionic Systems","authors":"I. Lyris, P. Lykourgias, A. I. Karanikas","doi":"10.1142/s1230161221500116","DOIUrl":"https://doi.org/10.1142/s1230161221500116","url":null,"abstract":"In this work we study the reduced dynamics of a system embedded in a quantum environment, with the use of correlation functions produced through appropriately defined reduced generating functionals. Our construction is based on expressing these functionals in terms of consistently defined coherent-state path integrals in the framework of the Keldysh-Schwinger out-of-equilibrium formalism.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"15 1","pages":"2150011:1-2150011:32"},"PeriodicalIF":0.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87880041","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 : 2021-09-01DOI: 10.1142/S1230161221500128
M. Matolcsi, M. Weiner
Suppose that for some unit vectors [Formula: see text] in [Formula: see text] we have that for any [Formula: see text] [Formula: see text] is either orthogonal to [Formula: see text] or [Formula: see text] (i.e., [Formula: see text] and [Formula: see text] are unbiased). We prove that if [Formula: see text], then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into [Formula: see text] orthonormal bases, all being mutually unbiased with respect to each other.
{"title":"A Rigidity Property of Complete Systems of Mutually Unbiased Bases","authors":"M. Matolcsi, M. Weiner","doi":"10.1142/S1230161221500128","DOIUrl":"https://doi.org/10.1142/S1230161221500128","url":null,"abstract":"Suppose that for some unit vectors [Formula: see text] in [Formula: see text] we have that for any [Formula: see text] [Formula: see text] is either orthogonal to [Formula: see text] or [Formula: see text] (i.e., [Formula: see text] and [Formula: see text] are unbiased). We prove that if [Formula: see text], then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into [Formula: see text] orthonormal bases, all being mutually unbiased with respect to each other.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"163 1","pages":"2150012:1-2150012:6"},"PeriodicalIF":0.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80283340","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 : 2021-09-01DOI: 10.1142/s123016122150013x
S. Qamar, S. Cong, Kezhi Li, Zhixiang Dong, F. Shuang
In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.
{"title":"Nonlinear Optimal Feedback Control of the Two-Level Open Non-Markovian Stochastic Quantum System","authors":"S. Qamar, S. Cong, Kezhi Li, Zhixiang Dong, F. Shuang","doi":"10.1142/s123016122150013x","DOIUrl":"https://doi.org/10.1142/s123016122150013x","url":null,"abstract":"In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"4 1","pages":"2150013:1-2150013:26"},"PeriodicalIF":0.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72757586","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 : 2021-09-01DOI: 10.1142/s1230161221500141
Taihei Takahash, Noboru Watanabe
In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual entropy type complexity to be able to study the efficiency of information transmission for more general input Gaussian measures and Gaussian channels.
{"title":"A Note on Improved Treatment of Gaussian Communication Process","authors":"Taihei Takahash, Noboru Watanabe","doi":"10.1142/s1230161221500141","DOIUrl":"https://doi.org/10.1142/s1230161221500141","url":null,"abstract":"In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual entropy type complexity to be able to study the efficiency of information transmission for more general input Gaussian measures and Gaussian channels.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"2 1","pages":"2150014:1-2150014:33"},"PeriodicalIF":0.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75574183","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 : 2021-06-01DOI: 10.1142/s1230161221500062
Xiuhong Sun, Yuan Li
In this note, we mainly study the necessary and sufficient conditions for the complete positivity of generalizations of depolarizing and transpose-depolarizing channels. Specifically, we define [Formula: see text] and [Formula: see text], where [Formula: see text] (the set of all bounded linear operators on the finite-dimensional Hilbert space [Formula: see text] is given and [Formula: see text] is the transpose of [Formula: see text] in a fixed orthonormal basis of [Formula: see text] First, we show that [Formula: see text] is completely positive if and only if [Formula: see text] is a positive map, which is equivalent to [Formula: see text] Moreover, [Formula: see text] is a completely positive map if and only if [Formula: see text] and [Formula: see text] At last, we also get that [Formula: see text] is a completely positive map if and only if [Formula: see text] with [Formula: see text] for all [Formula: see text] where [Formula: see text] are eigenvalues of [Formula: see text].
{"title":"Complete Positivity of Two Class of Maps Involving Depolarizing and Transpose-Depolarizing Channels","authors":"Xiuhong Sun, Yuan Li","doi":"10.1142/s1230161221500062","DOIUrl":"https://doi.org/10.1142/s1230161221500062","url":null,"abstract":"In this note, we mainly study the necessary and sufficient conditions for the complete positivity of generalizations of depolarizing and transpose-depolarizing channels. Specifically, we define [Formula: see text] and [Formula: see text], where [Formula: see text] (the set of all bounded linear operators on the finite-dimensional Hilbert space [Formula: see text] is given and [Formula: see text] is the transpose of [Formula: see text] in a fixed orthonormal basis of [Formula: see text] First, we show that [Formula: see text] is completely positive if and only if [Formula: see text] is a positive map, which is equivalent to [Formula: see text] Moreover, [Formula: see text] is a completely positive map if and only if [Formula: see text] and [Formula: see text] At last, we also get that [Formula: see text] is a completely positive map if and only if [Formula: see text] with [Formula: see text] for all [Formula: see text] where [Formula: see text] are eigenvalues of [Formula: see text].","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"60 1","pages":"2150006:1-2150006:16"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87105955","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 : 2021-06-01DOI: 10.1142/s1230161221500098
P. Lugiewicz, R. Olkiewicz
We present a new one-parameter family of extremal positive maps on the three-dimensional matrix algebra. The new elements are characterized as mappings that preserve a one-dimensional orthogonal projector.
在三维矩阵代数上给出了一种新的单参数极值正映射族。新元素的特征是保持一维正交投影的映射。
{"title":"On a New Family of Extremal Positive Maps of Three-Dimensional Matrix Algebra","authors":"P. Lugiewicz, R. Olkiewicz","doi":"10.1142/s1230161221500098","DOIUrl":"https://doi.org/10.1142/s1230161221500098","url":null,"abstract":"We present a new one-parameter family of extremal positive maps on the three-dimensional matrix algebra. The new elements are characterized as mappings that preserve a one-dimensional orthogonal projector.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"107 1","pages":"2150009:1-2150009:11"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79357450","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 : 2021-06-01DOI: 10.1142/s1230161221500086
P. Lugiewicz, R. Olkiewicz
A class of bistochastic maps of three-dimensional matrix algebra which preserves a one-dimensional projector is studied.
研究了一类保留一维投影的三维矩阵代数双随机映射。
{"title":"On Extremal Positive Maps of Three-Dimensional Matrix Algebra","authors":"P. Lugiewicz, R. Olkiewicz","doi":"10.1142/s1230161221500086","DOIUrl":"https://doi.org/10.1142/s1230161221500086","url":null,"abstract":"A class of bistochastic maps of three-dimensional matrix algebra which preserves a one-dimensional projector is studied.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"43 1","pages":"2150008:1-2150008:22"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73535218","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 : 2021-06-01DOI: 10.1142/s1230161221500074
Jie Sun, Songfeng Lu
Recently, Okuyama and Ohzek [1] derived a speed limit for the imaginary-time Schrödinger equation, which is inspired by the prior work of Kieu, who had shown a new class of time–energy uncertainty relations suitable for actually evaluating the speed limit of quantum dynamics. In this paper, we apply the result of Okuyama and Ohzek to obtain a generalized speed limit for Grover’s search in imaginary-time quantum annealing. An estimate of the lower bound on the computational time is shown, from which the role of the coefficient function corresponding to the final Hamiltonian played in the quantum dynamics for the problem is sticking out. However, when trying to apply the speed limit to the analogue of Grover’s problem, we find that not only the coefficient of the target Hamiltonian is related to the time complexity of the algorithm, but also the coefficient of the initial Hamiltonian is crucial for determining the time complexity. This is new and generalizes one of the results in our previous work.
{"title":"On the Speed Limit for Imaginary-Time Schrödinger Equation with Application to Quantum Searches","authors":"Jie Sun, Songfeng Lu","doi":"10.1142/s1230161221500074","DOIUrl":"https://doi.org/10.1142/s1230161221500074","url":null,"abstract":"Recently, Okuyama and Ohzek [1] derived a speed limit for the imaginary-time Schrödinger equation, which is inspired by the prior work of Kieu, who had shown a new class of time–energy uncertainty relations suitable for actually evaluating the speed limit of quantum dynamics. In this paper, we apply the result of Okuyama and Ohzek to obtain a generalized speed limit for Grover’s search in imaginary-time quantum annealing. An estimate of the lower bound on the computational time is shown, from which the role of the coefficient function corresponding to the final Hamiltonian played in the quantum dynamics for the problem is sticking out. However, when trying to apply the speed limit to the analogue of Grover’s problem, we find that not only the coefficient of the target Hamiltonian is related to the time complexity of the algorithm, but also the coefficient of the initial Hamiltonian is crucial for determining the time complexity. This is new and generalizes one of the results in our previous work.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"67 1","pages":"2150007:1-2150007:9"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79110774","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 : 2021-06-01DOI: 10.1142/s1230161221500050
M. Rosa, J. C. García-Corte, F. Guerrero-Poblet
We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.
{"title":"Uniform and Completely Nonequilibrium Invariant States for Weak Coupling Limit Type Quantum Markov Semigroups Associated with Eulerian Cycles","authors":"M. Rosa, J. C. García-Corte, F. Guerrero-Poblet","doi":"10.1142/s1230161221500050","DOIUrl":"https://doi.org/10.1142/s1230161221500050","url":null,"abstract":"We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"113 1","pages":"2150005:1-2150005:21"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80210716","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 : 2021-01-15DOI: 10.21203/RS.3.RS-143923/V1
Irina Basieva, A. Khrennikov
Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this paper, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed toorder preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preservethe order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment ℰ: 1) entropy (disorder) increasing in the process of adaptation to the specific features of ℰ; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.
{"title":"\"What Is Life?\": Open Quantum Systems Approach","authors":"Irina Basieva, A. Khrennikov","doi":"10.21203/RS.3.RS-143923/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-143923/V1","url":null,"abstract":"\u0000 Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this paper, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed toorder preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preservethe order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment ℰ: 1) entropy (disorder) increasing in the process of adaptation to the specific features of ℰ; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"11 1","pages":"2250016:1-2250016:25"},"PeriodicalIF":0.8,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86109311","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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