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Research School;Mathematical Physics
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the basic quantum optical systems and concepts as ’closed’ (i.e. isolated) quantum systems. We start with laser driven two-level atoms, the Jaynes-Cummings model of Cavity Quantum Electro-dynamics, and illustrate with the example of trapped ions control of the quantum motion of atoms via laser light. This will lead us to the model system of an ion trap quantum computer where we employ control ideas to design quantum gates.
In the second part of the course we will consider open quantum optical systems. Here the system of interest is coupled to a bosonic bath or environment (e.g. vacuum modes of the radiation field), providing damping and decoherence. We will develop the theory for the example of a radiatively damped two-level atom, and derive the corresponding master equation, and discuss its solution and physical interpretation. On a more advanced level, and as link to the mathematical literature, we establish briefly the connection to topics like continuous measurement theory (of photon counting), the Quantum Stochastic Schrödinger Equation, and quantum trajectories (here as as time evolution of a radiatively damped atom conditional to observing a given photon count trajectory). As an example of the application of the formalism we discuss quantum state transfer in a quantum optical network.
Parts of this video related to ongoing unpublished research have been cut off.
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the ...
81P68 ; 81V80
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- 358 p.
ISBN 978-0-8218-2084-1
Proceedings of symposia in applied mathematics , 0058
Localisation : Collection 1er étage
théorie quantique # calcul quantique # algorithme quantique # complexité quantique # code correcteur d'erreur # cryptographie quantique
81-01 ; 81-02 ; 81P68 ; 68Q05 ; 94A60
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- 310 p.
ISBN 978-0-8218-2140-4
Contemporary mathematics , 0305
Localisation : Collection 1er étage
théorie quantique # théorie de l'information # calcul quantique # modèle de calcul # groupe # algèbre # cryptographie
81-06 ; 94-06 ; 81P68
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- 224 p.
ISBN 978-0-8218-3202-8
Contemporary mathematics , 0317
Localisation : Collection 1er étage
analyse fonctionnelle # Gross # analyse fonctionnelle non linéaire # analyse dimensionnelle # EDP stochastique # analyse de bruit # mouvement brownien # analyse de Segal-Bargmann # noyau de la chaleur # application
60H40 ; 28C20 ; 60G20 ; 46N50 ; 46L52 ; 58J35 ; 31C25 ; 62P05 ; 81P68 ; 81S30
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- 211 p.
ISBN 978-0-8218-3330-8
CRM proceedings & lecture notes , 0033
Localisation : Collection 1er étage
système dynamique différentiable # géométrie algébrique # EDP # propriété de Kowaleski # singularité # équation de Painlevé # déformation isomonodromique # système complètement intégrable # soliton # monodromie
81D07 ; 49J20 ; 81V10 ; 81V80 ; 78A60 ; 81P68
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- 224 p.
ISBN 978-0-8218-3483-1
Contemporary mathematics , 0349
Localisation : Collection 1er étage
théorie des groupes # groupe de permutation # groupe non-abélien # théorie quantique # informatique # algorithme # groupe d'automorphisme # calcul quantique
20B40 ; 20E05 ; 20F28 ; 81P68 ; 68Q05 ; 68Q17 ; 68Q42 ; 68Q45 ; 68T05
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- 348 p.
ISBN 978-0-8218-3618-7
Contemporary mathematics , 0378
Localisation : Collection 1er étage
groupe libre # groupe fini # groupe infini # langage formel # mot infini # splitting # théorie combinatoire des groupes
20-06 ; 20B40 ; 20E05 ; 20F28 ; 81P68
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- 147 p.
ISBN 978-0-8218-3600-2
Contemporary mathematics , 0381
Localisation : Collection 1er étage
théorie quantique # théorie des codes # calcul quantique # cryptographie # informatique # base de Gröbner # courbe algébrique
81P68 ; 68Q05 ; 94B05 ; 05E20
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- 380p.
ISBN 978-3-540-76891-3
Lecture notes in mathematics , 1931
Localisation : Collection 1er étage
groupe topologique # groupe de Lie # analyse harmonique abstraite # algèbre non-associative # algèbre de Lie # analyse globale # algorithme quantique
22-06 ; 43-06 ; 17-06 ; 58-06 ; 22Exx ; 43-XX ; 17Bxx ; 81P68 ; 00B25
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- 380 p.
ISBN 978-3-540-76891-3
Lecture notes in mathematics , 1931
Localisation : Collection 1er étage
groupe de Lie # analyse harmonique abstraite # espace symétrique # groupe semi simple # analyse globale # correspondance Langlands # groupe algébrique complexe # cryptographie quantique # calcul numérique quantique
22Exx ; 43-06 ; 17Bxx ; 58-06 ; 81P68
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- vii; 240 p.
ISBN 978-0-8218-4627-8
Contemporary mathematics , 0482
Localisation : Collection 1er étage
théorie quantique # communication quantique # théorie de la représentation # théorie des catégories
81P68 ; 81T18 ; 81V10 ; 68M07 ; 37F25 ; 20F36 ; 57M25 ; 57M27 ; 47N55
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- ix; 348 p.
ISBN 978-0-8218-4828-9
Proceedings of symposia in applied mathematics , 0068
Localisation : Collection 1er étage
théorie quantique # théorie de la mesure quantique # cohérence quantique # information quantique # algorithme quantique # topologie de faible dimension # représentation de groupe # application à la physique
81P15 ; 81P68 ; 68Q12 ; 57M25 ; 57M27 ; 20C35 ; 81-06 ; 57Mxx ; 00B25
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- vii; 152 p.
ISBN 978-0-8218-4975-0
Contemporary mathematics , 0536
Localisation : Collection 1er étage
théorie quantique # calcul quantique
81P68 ; 81-01 ; 81-02 ; 81-06 ; 00B25
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Research School;Mathematical Physics
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the basic quantum optical systems and concepts as ’closed’ (i.e. isolated) quantum systems. We start with laser driven two-level atoms, the Jaynes-Cummings model of Cavity Quantum Electro-dynamics, and illustrate with the example of trapped ions control of the quantum motion of atoms via laser light. This will lead us to the model system of an ion trap quantum computer where we employ control ideas to design quantum gates.
In the second part of the course we will consider open quantum optical systems. Here the system of interest is coupled to a bosonic bath or environment (e.g. vacuum modes of the radiation field), providing damping and decoherence. We will develop the theory for the example of a radiatively damped two-level atom, and derive the corresponding master equation, and discuss its solution and physical interpretation. On a more advanced level, and as link to the mathematical literature, we establish briefly the connection to topics like continuous measurement theory (of photon counting), the Quantum Stochastic Schrödinger Equation, and quantum trajectories (here as as time evolution of a radiatively damped atom conditional to observing a given photon count trajectory). As an example of the application of the formalism we discuss quantum state transfer in a quantum optical network.
Parts of this video related to ongoing unpublished research have been cut off.
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the ...
81P68 ; 81V80
... Lire [+]
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
Research School;Mathematical Physics
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the basic quantum optical systems and concepts as ’closed’ (i.e. isolated) quantum systems. We start with laser driven two-level atoms, the Jaynes-Cummings model of Cavity Quantum Electro-dynamics, and illustrate with the example of trapped ions control of the quantum motion of atoms via laser light. This will lead us to the model system of an ion trap quantum computer where we employ control ideas to design quantum gates.
In the second part of the course we will consider open quantum optical systems. Here the system of interest is coupled to a bosonic bath or environment (e.g. vacuum modes of the radiation field), providing damping and decoherence. We will develop the theory for the example of a radiatively damped two-level atom, and derive the corresponding master equation, and discuss its solution and physical interpretation. On a more advanced level, and as link to the mathematical literature, we establish briefly the connection to topics like continuous measurement theory (of photon counting), the Quantum Stochastic Schrödinger Equation, and quantum trajectories (here as as time evolution of a radiatively damped atom conditional to observing a given photon count trajectory). As an example of the application of the formalism we discuss quantum state transfer in a quantum optical network.
Parts of this video related to ongoing unpublished research have been cut off.
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the ...
81P68 ; 81V80
... Lire [+]
Déposez votre fichier ici pour le déplacer vers cet enregistrement.
Research School;Mathematical Physics
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the basic quantum optical systems and concepts as ’closed’ (i.e. isolated) quantum systems. We start with laser driven two-level atoms, the Jaynes-Cummings model of Cavity Quantum Electro-dynamics, and illustrate with the example of trapped ions control of the quantum motion of atoms via laser light. This will lead us to the model system of an ion trap quantum computer where we employ control ideas to design quantum gates.
In the second part of the course we will consider open quantum optical systems. Here the system of interest is coupled to a bosonic bath or environment (e.g. vacuum modes of the radiation field), providing damping and decoherence. We will develop the theory for the example of a radiatively damped two-level atom, and derive the corresponding master equation, and discuss its solution and physical interpretation. On a more advanced level, and as link to the mathematical literature, we establish briefly the connection to topics like continuous measurement theory (of photon counting), the Quantum Stochastic Schrödinger Equation, and quantum trajectories (here as as time evolution of a radiatively damped atom conditional to observing a given photon count trajectory). As an example of the application of the formalism we discuss quantum state transfer in a quantum optical network.
Parts of this video related to ongoing unpublished research have been cut off.
Quantum optical systems provides one of the best physical settings to engineer quantum many-body systems of atoms and photons, which can be controlled and measured on the level of single quanta. In this course we will provide an introduction to quantum optics from the perspective of control and measurement, and in light of possible applications including quantum computing and quantum communication.
The first part of the course will introduce the ...
81P68 ; 81V80
... Lire [+]
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Research talks;Mathematical Physics
Combining the relativistic speed limit on transmitting information with linearity and unitarity of quantum mechanics leads to a relativistic extension of the no-cloning principle called spacetime replication of quantum information. We introduce continuous-variable spacetime-replication protocols, expressed in a Gaussian-state basis, that build on novel homologically constructed continuous-variable quantum error correcting codes. Compared to qubit encoding, our continuous-variable solution requires half as many shares per encoded system. We show an explicit construction for the five-mode case and how it can be implemented experimentally. As well we analyze the ramifications of finite squeezing on the protocol.
Combining the relativistic speed limit on transmitting information with linearity and unitarity of quantum mechanics leads to a relativistic extension of the no-cloning principle called spacetime replication of quantum information. We introduce continuous-variable spacetime-replication protocols, expressed in a Gaussian-state basis, that build on novel homologically constructed continuous-variable quantum error correcting codes. Compared to ...
81P45 ; 81P68
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- 128 p.
ISBN 978-81-7319-688-1
Localisation : Ouvrage RdC (PART)
probabilité quantique # circuit # pont quantique # transformation de Fourier # code correcteur d'erreur # algorithme de Shor # théorie de l'information # calcul quantique
81P68 ; 94Bxx ; 94A15
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