Pub Date : 2023-05-12DOI: 10.1142/S123016122380001X
E. Aurell, R. Kawai
In 1983 Göran Lindblad published a monograph on nonequilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are realized in the real world. The second is that Lindblad’s proposal for thermodynamic entropy (as opposed to information-theoretic entropy) foreshadows much more recent investigations into optimal quantum transport which is a current research focus in several fields.
{"title":"A Perspective on Lindblad's Non-Equilibrium Entropy","authors":"E. Aurell, R. Kawai","doi":"10.1142/S123016122380001X","DOIUrl":"https://doi.org/10.1142/S123016122380001X","url":null,"abstract":"In 1983 Göran Lindblad published a monograph on nonequilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are realized in the real world. The second is that Lindblad’s proposal for thermodynamic entropy (as opposed to information-theoretic entropy) foreshadows much more recent investigations into optimal quantum transport which is a current research focus in several fields.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"69 1","pages":"2380001:1-2380001:31"},"PeriodicalIF":0.8,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79978032","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 : 2023-04-06DOI: 10.1142/S1230161223500075
W. Tarnowski, Dariusz Chru'sci'nski, S. Denisov, K. Życzkowski
We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.
{"title":"Random Lindblad Operators Obeying Detailed Balance","authors":"W. Tarnowski, Dariusz Chru'sci'nski, S. Denisov, K. Życzkowski","doi":"10.1142/S1230161223500075","DOIUrl":"https://doi.org/10.1142/S1230161223500075","url":null,"abstract":"We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"13 1","pages":"2350007:1-2350007:32"},"PeriodicalIF":0.8,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86733487","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 : 2023-03-01DOI: 10.1142/S1230161223500051
F. V. Ende, Emanuel Malvetti, G. Dirr, T. Schulte-Herbrüggen
Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system (“toy model”) on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of [Formula: see text]-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.
{"title":"Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources","authors":"F. V. Ende, Emanuel Malvetti, G. Dirr, T. Schulte-Herbrüggen","doi":"10.1142/S1230161223500051","DOIUrl":"https://doi.org/10.1142/S1230161223500051","url":null,"abstract":"Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian counterparts for the case of a single qubit. Second, we use this description in the framework of bilinear control systems to characterise reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath. The core problem reduces to studying a hybrid control system (“toy model”) on the standard simplex allowing for two types of evolution: (i) instantaneous permutations and (ii) a one-parameter semigroup of [Formula: see text]-stochastic maps. We generalise upper bounds of the reachable set of this toy model invoking new results on thermomajorisation. Using tools of control theory we fully characterise these reachable sets as well as the set of stabilisable states as exemplified by exact results in qutrit systems.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"1 1","pages":"2350005:1-2350005:53"},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83653794","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 : 2023-03-01DOI: 10.1142/s1230161223500026
J. R. Bolaños-Servín, R. Quezada, Josué Vázquez-Becerra
We broaden the study of circulant Quantum Markov Semigroups (QMS). First, we introduce the notions of [Formula: see text]-circulant GKSL generator and [Formula: see text]-circulant QMS from the circulant case, corresponding to [Formula: see text], to an arbitrary finite group [Formula: see text]. Second, we show that each [Formula: see text]-circulant GKSL generator has a block-diagonal representation [Formula: see text], where [Formula: see text] is a [Formula: see text]-circulant matrix determined by some [Formula: see text]. Denoting by [Formula: see text] the subgroup of [Formula: see text] generated by the support of [Formula: see text], we prove that [Formula: see text] has its own block-diagonal matrix representation [Formula: see text] where [Formula: see text] is an irreducible [Formula: see text]-circulant matrix and [Formula: see text] is the index of [Formula: see text] in [Formula: see text]. Finally, we exploit such block representations to characterize the structure, steady states, and asymptotic evolution of [Formula: see text]-circulant QMSs.
{"title":"G-Circulant Quantum Markov Semigroups","authors":"J. R. Bolaños-Servín, R. Quezada, Josué Vázquez-Becerra","doi":"10.1142/s1230161223500026","DOIUrl":"https://doi.org/10.1142/s1230161223500026","url":null,"abstract":"We broaden the study of circulant Quantum Markov Semigroups (QMS). First, we introduce the notions of [Formula: see text]-circulant GKSL generator and [Formula: see text]-circulant QMS from the circulant case, corresponding to [Formula: see text], to an arbitrary finite group [Formula: see text]. Second, we show that each [Formula: see text]-circulant GKSL generator has a block-diagonal representation [Formula: see text], where [Formula: see text] is a [Formula: see text]-circulant matrix determined by some [Formula: see text]. Denoting by [Formula: see text] the subgroup of [Formula: see text] generated by the support of [Formula: see text], we prove that [Formula: see text] has its own block-diagonal matrix representation [Formula: see text] where [Formula: see text] is an irreducible [Formula: see text]-circulant matrix and [Formula: see text] is the index of [Formula: see text] in [Formula: see text]. Finally, we exploit such block representations to characterize the structure, steady states, and asymptotic evolution of [Formula: see text]-circulant QMSs.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"54 1","pages":"2350002:1-2350002:29"},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80867383","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 : 2023-03-01DOI: 10.1142/s123016122350004x
A. Riahi, H. Rebei, Amine Ettaieb, Z. Alhussain, H. Elmonser
The main purpose of this paper is to investigate a generalized oscillator algebra, naturally associated with the [Formula: see text]-Lévy-Meixner polynomials. We solve the problem of the Hopf algebraic structure for the [Formula: see text]-deformed Lévy-Meixner oscillator algebra based on the one-parameter deformation of canonical commutation relations.
{"title":"Hopf Structure for the q-Lévy-Meixner Oscillator Algebra","authors":"A. Riahi, H. Rebei, Amine Ettaieb, Z. Alhussain, H. Elmonser","doi":"10.1142/s123016122350004x","DOIUrl":"https://doi.org/10.1142/s123016122350004x","url":null,"abstract":"The main purpose of this paper is to investigate a generalized oscillator algebra, naturally associated with the [Formula: see text]-Lévy-Meixner polynomials. We solve the problem of the Hopf algebraic structure for the [Formula: see text]-deformed Lévy-Meixner oscillator algebra based on the one-parameter deformation of canonical commutation relations.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"116 1 1","pages":"2350004:1-2350004:18"},"PeriodicalIF":0.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82790682","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 : 2023-02-01DOI: 10.1142/s1230161222500160
Irina Basieva, Andrei Khrennikov
Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in 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-modelling. In this paper, we turn to the famous Schrödinger’s book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed to order 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 preserve the 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 : 1) entropy (disorder) increasing in the process of adaptation to the specific features of ; 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, Andrei Khrennikov","doi":"10.1142/s1230161222500160","DOIUrl":"https://doi.org/10.1142/s1230161222500160","url":null,"abstract":"<p>Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in 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-modelling. In this paper, we turn to the famous Schrödinger’s book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed to order 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 preserve the 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 <i>the camel-like graphs for entropy-evolution</i> in the process of interaction with a new environment <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℰ</mi></math></span><span></span>: 1) entropy (disorder) increasing in the process of adaptation to the specific features of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℰ</mi></math></span><span></span>; 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.</p>","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"239 ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507237","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 : 2022-12-01DOI: 10.1142/s1230161222500184
L. Accardi, Tarek Hamdi, Y. Lu
In the first part of the present paper, we have proved that, in order to find an explicit expression for the action, on the [Formula: see text]-orthogonal polynomials, of the 1-parameter unitary groups [Formula: see text] and [Formula: see text], the solution of the inverse normal order problem on the quantum algebra canonically associated to the classical semi-circle random variable is required. In this paper we solve this problem. The solution is obtained in two steps. First we determine the explicit form of normal order in the more general framework of [Formula: see text]-mode-type interacting Fock spaces. Then this result is applied to solve the inverse normal order problem in the semi-circle case.
{"title":"The Quantum Mechanics Canonically Associated to Free Probability II: The Normal and Inverse Normal Order Problem","authors":"L. Accardi, Tarek Hamdi, Y. Lu","doi":"10.1142/s1230161222500184","DOIUrl":"https://doi.org/10.1142/s1230161222500184","url":null,"abstract":"In the first part of the present paper, we have proved that, in order to find an explicit expression for the action, on the [Formula: see text]-orthogonal polynomials, of the 1-parameter unitary groups [Formula: see text] and [Formula: see text], the solution of the inverse normal order problem on the quantum algebra canonically associated to the classical semi-circle random variable is required. In this paper we solve this problem. The solution is obtained in two steps. First we determine the explicit form of normal order in the more general framework of [Formula: see text]-mode-type interacting Fock spaces. Then this result is applied to solve the inverse normal order problem in the semi-circle case.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"22 1","pages":"2250018:1-2250018:31"},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74677297","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 : 2022-09-01DOI: 10.1142/S1230161222500111
M. Lewenstein, Guillem Muller-Rigat, Jordi Tura i Brugués, A. Sanpera
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [34], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an [Formula: see text]-qubit system by proposing linear maps that, when applied to any state, result in a biseparable state for the [Formula: see text] partitions, i.e., [Formula: see text]-entanglement depth. Furthermore, we derive criteria to detect arbitrary [Formula: see text]-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or [Formula: see text]-entanglement depth) conditions in the symmetric sector, including the diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps.
{"title":"Linear Maps as Sufficient Criteria for Entanglement Depth and Compatibility in Many-Body Systems","authors":"M. Lewenstein, Guillem Muller-Rigat, Jordi Tura i Brugués, A. Sanpera","doi":"10.1142/S1230161222500111","DOIUrl":"https://doi.org/10.1142/S1230161222500111","url":null,"abstract":"Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [34], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an [Formula: see text]-qubit system by proposing linear maps that, when applied to any state, result in a biseparable state for the [Formula: see text] partitions, i.e., [Formula: see text]-entanglement depth. Furthermore, we derive criteria to detect arbitrary [Formula: see text]-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or [Formula: see text]-entanglement depth) conditions in the symmetric sector, including the diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"47 1","pages":"2250011:1-2250011:23"},"PeriodicalIF":0.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74095466","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 : 2022-09-01DOI: 10.1142/S1230161222500159
M. Cattaneo, G. Giorgi, R. Zambrini, S. Maniscalco
The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.
{"title":"A Brief Journey through Collision Models for Multipartite Open Quantum Dynamics","authors":"M. Cattaneo, G. Giorgi, R. Zambrini, S. Maniscalco","doi":"10.1142/S1230161222500159","DOIUrl":"https://doi.org/10.1142/S1230161222500159","url":null,"abstract":"The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"31 1","pages":"2250015:1-2250015:26"},"PeriodicalIF":0.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84694129","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 : 2022-09-01DOI: 10.1142/s1230161222500147
V. Karimipour
We review the concept of the quasi-inverse of qubit channels and of higher dimensional channels. Quasi-inverse is a channel which when concatenaded to the original channel, increases its average fidelity in an optimal way. For qubit channels, we fully characterize the quasi-inverse, while for higher dimensional channels, we prove general theorems and provide bounds for the increased average fidelity. Nevertheless, explicit examples are given when exact quasi-inverses can be found.
{"title":"On Quasi-Inversion of Quantum Channels in 2 and in Higher Dimensions","authors":"V. Karimipour","doi":"10.1142/s1230161222500147","DOIUrl":"https://doi.org/10.1142/s1230161222500147","url":null,"abstract":"We review the concept of the quasi-inverse of qubit channels and of higher dimensional channels. Quasi-inverse is a channel which when concatenaded to the original channel, increases its average fidelity in an optimal way. For qubit channels, we fully characterize the quasi-inverse, while for higher dimensional channels, we prove general theorems and provide bounds for the increased average fidelity. Nevertheless, explicit examples are given when exact quasi-inverses can be found.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"88 1","pages":"2250014:1-2250014:21"},"PeriodicalIF":0.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88745180","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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