slides on Quantum Isometry Groups
... Early work : formulation of quantum automorphism and quantum permutation groups by Wang, and follow-up work by Banica, Bichon and others. Basic principle: For some given mathematical structure (e.g., a finite set, a graph, a C ∗ or von Neumann algebra) identify (if possible) the group of automorphis ...
... Early work : formulation of quantum automorphism and quantum permutation groups by Wang, and follow-up work by Banica, Bichon and others. Basic principle: For some given mathematical structure (e.g., a finite set, a graph, a C ∗ or von Neumann algebra) identify (if possible) the group of automorphis ...
Classification of completely positive maps
... Quantum mechanics is perhaps the primary triumph of 20th century physics. It is used in every subfield of physics and has broad applications to the other sciences and engineering. It is the way the microscopic world works. Without going into the full details of the remarkable range of quantum phenom ...
... Quantum mechanics is perhaps the primary triumph of 20th century physics. It is used in every subfield of physics and has broad applications to the other sciences and engineering. It is the way the microscopic world works. Without going into the full details of the remarkable range of quantum phenom ...
Properties
... Entanglement Distillation Carry Out Transformations involving Local Operations and Classical Communication Local operations act on A and one set of N qubits. Or B and the other set. ...
... Entanglement Distillation Carry Out Transformations involving Local Operations and Classical Communication Local operations act on A and one set of N qubits. Or B and the other set. ...
Quantum Statistical Response Functions
... Many experiments that one would like to describe theoretically have a common (idealised) form: one starts by perturbing the system one wants to study by an external agent (such as a laserpulse) and after a certain time interval one probes the system by measuring one of its dynamical variables such a ...
... Many experiments that one would like to describe theoretically have a common (idealised) form: one starts by perturbing the system one wants to study by an external agent (such as a laserpulse) and after a certain time interval one probes the system by measuring one of its dynamical variables such a ...
Spin Algebra, Spin Eigenvalues, Pauli Matrices Lecture 10
... But bbot (a) must be smaller than btop (a), so only the second solution works. Therefore bbot (a) = −btop (a). Hence b, which is the eigenvalue of Sz , ranges from −btop (a) to btop (a). Furthermore, since S− lowers this value by ~ each time it is applied, these two values must differ by an integer ...
... But bbot (a) must be smaller than btop (a), so only the second solution works. Therefore bbot (a) = −btop (a). Hence b, which is the eigenvalue of Sz , ranges from −btop (a) to btop (a). Furthermore, since S− lowers this value by ~ each time it is applied, these two values must differ by an integer ...
Operator Quantum Error Correction.
... with dim(HA ) = m, dim(HB ) = n and dim K = dim H − mn. We shall write σ A for operators in B(HA ) and σ B for operators in B(HB ). Thus the restriction of the noise commutant A0 to HA ⊗ HB consists of the operators of the form σ = 1lA ⊗ σ B where 1lA is the identity element of B(HA ). For notationa ...
... with dim(HA ) = m, dim(HB ) = n and dim K = dim H − mn. We shall write σ A for operators in B(HA ) and σ B for operators in B(HB ). Thus the restriction of the noise commutant A0 to HA ⊗ HB consists of the operators of the form σ = 1lA ⊗ σ B where 1lA is the identity element of B(HA ). For notationa ...
Jaynes-Cummings model
... A 2-level atom has a Hilbert space spanned by two energy eigenstates: a lower-energy “ground” state |gi and an excited state |ei. Because it consists of only a 2-dimensional Hilbert space, it is mathematically equivalent to a spin-1/2 particle. Just as for the spin-1/2 particle, we can think of a st ...
... A 2-level atom has a Hilbert space spanned by two energy eigenstates: a lower-energy “ground” state |gi and an excited state |ei. Because it consists of only a 2-dimensional Hilbert space, it is mathematically equivalent to a spin-1/2 particle. Just as for the spin-1/2 particle, we can think of a st ...
