A short introduction to unitary 2-designs
... years. Many mathematical and physical structures, such as Latin squares, affine and projective planes, mutually unbiased bases, error correcting codes, and so much more, can be ultimately be shown to be some type of design. In most of these cases, the associated designs are combinatorial designs. Th ...
... years. Many mathematical and physical structures, such as Latin squares, affine and projective planes, mutually unbiased bases, error correcting codes, and so much more, can be ultimately be shown to be some type of design. In most of these cases, the associated designs are combinatorial designs. Th ...
Transposition in Quantum Information Theory
... in order to preserve the trace of quantum states. The completely positivity might not be that clear on first sight. It is not enough to assume T : Mn → Mm to be positive and trace-preserving. We cannot define a matrix space of the whole universe, whatever this is. Therefore we would like to have a l ...
... in order to preserve the trace of quantum states. The completely positivity might not be that clear on first sight. It is not enough to assume T : Mn → Mm to be positive and trace-preserving. We cannot define a matrix space of the whole universe, whatever this is. Therefore we would like to have a l ...
Composing Quantum Protocols in a Classical Environment
... quantum protocols formalized by quantum operators with classical in- and output for the honest players, see Figure 1. For an honest player, say Alice, the jth protocol outputs an index i indicating which functionality is to be called, classical auxiliary (or “state”) information information Sj and a ...
... quantum protocols formalized by quantum operators with classical in- and output for the honest players, see Figure 1. For an honest player, say Alice, the jth protocol outputs an index i indicating which functionality is to be called, classical auxiliary (or “state”) information information Sj and a ...
Quantum Channels - Institut Camille Jordan
... an orthonormal basis (fi )i∈J where the set J contains the original set I; we b of V from H ⊗ K onto itself. have obtained a unitary extension V We want now to prove that they provide the announced quantum channel. Let T be a trace class operator, which we first assume to be a pure state |ψihψ|. If ...
... an orthonormal basis (fi )i∈J where the set J contains the original set I; we b of V from H ⊗ K onto itself. have obtained a unitary extension V We want now to prove that they provide the announced quantum channel. Let T be a trace class operator, which we first assume to be a pure state |ψihψ|. If ...
Quantum Teleportation
... exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it. The teleportation technique makes use of quantum entanglemant. Clouds of trillions of atoms have for the first time being linked by quantum entanglement that spooky almost telepathic lin ...
... exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it. The teleportation technique makes use of quantum entanglemant. Clouds of trillions of atoms have for the first time being linked by quantum entanglement that spooky almost telepathic lin ...
Quantum Probability Quantum Information Theory Quantum
... martingales, Markov chains, . . .) for a long time remained completely separated from the mathematical language of quantum mechanics (vectors in a Hilbert space, hermitian operators, unitary transformations, . . .). In the 1970’s and 1980’s people such as Accardi, Lewis, Davies, Kümmerer, building ...
... martingales, Markov chains, . . .) for a long time remained completely separated from the mathematical language of quantum mechanics (vectors in a Hilbert space, hermitian operators, unitary transformations, . . .). In the 1970’s and 1980’s people such as Accardi, Lewis, Davies, Kümmerer, building ...
Momentum Maps, Dual Pairs and Reduction in
... i ωi ~ , ωi closed 2forms on M , we can define a corresponding star product ? by means of Fedosov’s contruction [10]. The equivalence class of this star product does not depend upon the choice of symplectic connection. It does depend though on the deRham cohomology classes [ωi ] ∈ H 2 (M ). In fact, ...
... i ωi ~ , ωi closed 2forms on M , we can define a corresponding star product ? by means of Fedosov’s contruction [10]. The equivalence class of this star product does not depend upon the choice of symplectic connection. It does depend though on the deRham cohomology classes [ωi ] ∈ H 2 (M ). In fact, ...
A quantum computing primer for operator theorists
... the subspace {λ|ψ : λ ∈ C} is written |ψψ|. Further let B(H) be the collection of operators which act on H. We will use the physics convention U † for the adjoint of an operator U . The study of operators on Hilbert space is central to the theory of quantum mechanics. For instance, consider the f ...
... the subspace {λ|ψ : λ ∈ C} is written |ψψ|. Further let B(H) be the collection of operators which act on H. We will use the physics convention U † for the adjoint of an operator U . The study of operators on Hilbert space is central to the theory of quantum mechanics. For instance, consider the f ...
Analysis of a Quantum Error Correcting Code using Quantum
... addition of primitive operations for quantum information processing. The general picture is that a system consists of a number of independent components, or processes, which can communicate by sending data along channels. In particular, qubits can be transmitted on channels. One of the distinctive f ...
... addition of primitive operations for quantum information processing. The general picture is that a system consists of a number of independent components, or processes, which can communicate by sending data along channels. In particular, qubits can be transmitted on channels. One of the distinctive f ...