Pub Date : 2024-01-23DOI: 10.1142/s1230161223500191
Yusuke Sawada
Wildberger introduced the method of constructing a Hermitian discrete hypergroup from a random walk on a graph. In this study, we will apply his method to an open quantum random walk (OQRW) on a distance set and show that any discrete hypergroup that is not necessarily Hermitian can be realized using the OQRW on a distance set. We also investigate the distributions of OQRWs on distance sets in the view point of hypergroups.
{"title":"Hypergroup Structures of Open Quantum Random Walks on Distance Sets","authors":"Yusuke Sawada","doi":"10.1142/s1230161223500191","DOIUrl":"https://doi.org/10.1142/s1230161223500191","url":null,"abstract":"<p>Wildberger introduced the method of constructing a Hermitian discrete hypergroup from a random walk on a graph. In this study, we will apply his method to an open quantum random walk (OQRW) on a distance set and show that any discrete hypergroup that is not necessarily Hermitian can be realized using the OQRW on a distance set. We also investigate the distributions of OQRWs on distance sets in the view point of hypergroups.</p>","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156413","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 : 2023-09-01DOI: 10.1142/s1230161223500129
R. Alicki
Göran Lindblad was one of the pioneers of what is now called quantum thermodynamics. From this vast and rapidly developing field, we have selected a sample of results concerning quantum open systems described by Markovian master equations of the Lindblad (Gorini–Kossakowski–Sudarshan) type, which are applied to models of lasers. One can study their thermodynamics using the properties of quantum relative entropy, also introduced by Lindblad.
{"title":"Thermodynamics of Markovian Open Quantum Systems with Application to Lasers","authors":"R. Alicki","doi":"10.1142/s1230161223500129","DOIUrl":"https://doi.org/10.1142/s1230161223500129","url":null,"abstract":"Göran Lindblad was one of the pioneers of what is now called quantum thermodynamics. From this vast and rapidly developing field, we have selected a sample of results concerning quantum open systems described by Markovian master equations of the Lindblad (Gorini–Kossakowski–Sudarshan) type, which are applied to models of lasers. One can study their thermodynamics using the properties of quantum relative entropy, also introduced by Lindblad.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738331","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 : 2023-09-01DOI: 10.1142/s1230161223500117
Vinayak Jagadish, R. Srikanth, Francesco Petruccione
It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.
{"title":"Initial Correlations and Complete Positivity of Dynamical Maps","authors":"Vinayak Jagadish, R. Srikanth, Francesco Petruccione","doi":"10.1142/s1230161223500117","DOIUrl":"https://doi.org/10.1142/s1230161223500117","url":null,"abstract":"It is now increasingly realized in the study of open system dynamics that initial correlations do not pose a conceptual difficulty as traditionally believed. A similar methodology as used to describe initial product states can be adopted, with the only difference being that the reduced dynamics is possibly not completely positive, entailing that only a restricted set of initial reduced states lead to a physically valid dynamics. Here we study the interplay between the initial correlations, especially in the form of highly entangled states, and the system–environment unitary. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738332","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 : 2023-09-01DOI: 10.1142/s1230161223500154
Brecht I. C. Donvil, Paolo Muratore-Ginanneschi
It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation — a quantum master equation. Unraveling in quantum trajectories offers a picture of open system dynamics dual to solving master equations. In the unraveling picture, physical indicators are computed as Monte Carlo averages over a stochastic process valued in the Hilbert space of the system. This approach is particularly adapted to simulate systems in large Hilbert spaces. We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system described by a Markov process generated by ordinary stochastic differential equations for which rigorous concentration estimates are available. The unraveling can be equivalently formulated in terms of norm-preserving state vectors or in terms of linear “ostensible” processes trace preserving only on average. We illustrate the results in the case of a two level system in a simple boson environment. Next, we derive the state-of-the-art form of the Diósi-Gisin-Strunz Gaussian random ostensible state equation in the context of a model problem. This equation provides an exact unraveling of open systems in Gaussian environments. We compare and contrast the two unravelings and their potential for applications to quantum error mitigation.
{"title":"On the Unraveling of Open Quantum Dynamics","authors":"Brecht I. C. Donvil, Paolo Muratore-Ginanneschi","doi":"10.1142/s1230161223500154","DOIUrl":"https://doi.org/10.1142/s1230161223500154","url":null,"abstract":"It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation — a quantum master equation. Unraveling in quantum trajectories offers a picture of open system dynamics dual to solving master equations. In the unraveling picture, physical indicators are computed as Monte Carlo averages over a stochastic process valued in the Hilbert space of the system. This approach is particularly adapted to simulate systems in large Hilbert spaces. We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system described by a Markov process generated by ordinary stochastic differential equations for which rigorous concentration estimates are available. The unraveling can be equivalently formulated in terms of norm-preserving state vectors or in terms of linear “ostensible” processes trace preserving only on average. We illustrate the results in the case of a two level system in a simple boson environment. Next, we derive the state-of-the-art form of the Diósi-Gisin-Strunz Gaussian random ostensible state equation in the context of a model problem. This equation provides an exact unraveling of open systems in Gaussian environments. We compare and contrast the two unravelings and their potential for applications to quantum error mitigation.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738333","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 : 2023-09-01DOI: 10.1142/s1230161223500130
Jukka Kiukas, Pekka Lahti, Juha-Pekka Pellonpää
We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing subsequently on describing emergent classicality under quantum decoherence. While decoherence in quantum states has been studied extensively in the past, the measurement side is much less understood — here we present and extend some recent results on this topic.
{"title":"Joint Measurability in Lindbladian Open Quantum Systems","authors":"Jukka Kiukas, Pekka Lahti, Juha-Pekka Pellonpää","doi":"10.1142/s1230161223500130","DOIUrl":"https://doi.org/10.1142/s1230161223500130","url":null,"abstract":"We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing subsequently on describing emergent classicality under quantum decoherence. While decoherence in quantum states has been studied extensively in the past, the measurement side is much less understood — here we present and extend some recent results on this topic.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738334","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 : 2023-09-01DOI: 10.1142/s1230161223500166
Adam Stokes, Hannah Riley, Ahsan Nazir
We describe the physical relativity of light and matter quantum subsystems, their correlations, and energy exchanges. We examine the most commonly adopted definitions of atoms and photons, noting the significant difference in their localisation properties when expressed in terms of primitive manifestly gauge-invariant and local fields. As a result, different behaviours for entanglement generation and energy exchange occur for different definitions. We explore such differences in detail using toy models of a single photonic mode interacting with one and two dipoles.
{"title":"The Gauge-Relativity of Quantum Light, Matter, and Information","authors":"Adam Stokes, Hannah Riley, Ahsan Nazir","doi":"10.1142/s1230161223500166","DOIUrl":"https://doi.org/10.1142/s1230161223500166","url":null,"abstract":"We describe the physical relativity of light and matter quantum subsystems, their correlations, and energy exchanges. We examine the most commonly adopted definitions of atoms and photons, noting the significant difference in their localisation properties when expressed in terms of primitive manifestly gauge-invariant and local fields. As a result, different behaviours for entanglement generation and energy exchange occur for different definitions. We explore such differences in detail using toy models of a single photonic mode interacting with one and two dipoles.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738330","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 : 2023-06-01DOI: 10.1142/S1230161223770012
Ingemar Bengtsson
This is a brief account of the life and work of Göran Lindblad.
这是对Göran林德布拉德的生活和工作的简要介绍。
{"title":"Göran Lindblad in Memoriam","authors":"Ingemar Bengtsson","doi":"10.1142/S1230161223770012","DOIUrl":"https://doi.org/10.1142/S1230161223770012","url":null,"abstract":"This is a brief account of the life and work of Göran Lindblad.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"415 1","pages":"2377001:1-2377001:9"},"PeriodicalIF":0.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73249302","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 : 2023-06-01DOI: 10.1142/S1230161223500087
J. Larson, Sofia Qvarfort
In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.
{"title":"Exceptional Points and Exponential Sensitivity for Periodically Driven Lindblad Equations","authors":"J. Larson, Sofia Qvarfort","doi":"10.1142/S1230161223500087","DOIUrl":"https://doi.org/10.1142/S1230161223500087","url":null,"abstract":"In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"6 1","pages":"2350008:1-2350008:21"},"PeriodicalIF":0.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88312673","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 : 2023-06-01DOI: 10.1142/s1230161223500063
G. Lindblad
An analysis of the quantum measurement problem is presented which is a modest modification of the standard one often called the Copenhagen interpretation. The starting assumption is that QM is universal, and that all evolutions are unitary. We must also assume that the set of evolutions is restricted to allow the existence of stable structures for the equipment in our laboratory, including the measurement devices. The devices need some macroscopic properties to make the outcomes of the experiments stable data. There should not exist superdevices capable of retrieving the information needed to reverse these evolutions. As a result the quantum coherences complementary to the outcomes of experiments will typically be inaccessible and there is no need to remove them by decoherence. We need devices designed such that the outcome of an experiment is indicated by a pointer with the property that it has a definite but random final state. We then find that the outcomes of experiments can be considered factual data, and random in a classical sense. They can be considered to happen in a single world.
{"title":"A Neo-Copenhagen Quantum Mechanics","authors":"G. Lindblad","doi":"10.1142/s1230161223500063","DOIUrl":"https://doi.org/10.1142/s1230161223500063","url":null,"abstract":"An analysis of the quantum measurement problem is presented which is a modest modification of the standard one often called the Copenhagen interpretation. The starting assumption is that QM is universal, and that all evolutions are unitary. We must also assume that the set of evolutions is restricted to allow the existence of stable structures for the equipment in our laboratory, including the measurement devices. The devices need some macroscopic properties to make the outcomes of the experiments stable data. There should not exist superdevices capable of retrieving the information needed to reverse these evolutions. As a result the quantum coherences complementary to the outcomes of experiments will typically be inaccessible and there is no need to remove them by decoherence. We need devices designed such that the outcome of an experiment is indicated by a pointer with the property that it has a definite but random final state. We then find that the outcomes of experiments can be considered factual data, and random in a classical sense. They can be considered to happen in a single world.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"34 1","pages":"2350006:1-2350006:22"},"PeriodicalIF":0.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74110755","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 : 2023-05-15DOI: 10.1142/S1230161223500099
J. Pekola, B. Karimi, M. Cattaneo, S. Maniscalco
We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], assuming that the qubit–bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.
{"title":"Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit","authors":"J. Pekola, B. Karimi, M. Cattaneo, S. Maniscalco","doi":"10.1142/S1230161223500099","DOIUrl":"https://doi.org/10.1142/S1230161223500099","url":null,"abstract":"We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of [Formula: see text] spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime [Formula: see text], assuming that the qubit–bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behaviour is captured by an analytical approximation that makes use of the property [Formula: see text] to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"14 1","pages":"2350009:1-2350009:18"},"PeriodicalIF":0.8,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89352453","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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