On quantum channels

Abstract

One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a quantum channel or completely positive map (CP-map) is the dual state associated to it. The present paper is a collection of well-known, less known and new results on quantum channels, presented in a unified way. We will show how this dual state induces nice characterizations of the extremal maps of the convex set of CP-maps, and how normal forms for states defined on a Hilbert space with a tensor product structure lead to interesting parameterizations of quantum channels.

References in corpus (22)

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Cited by in corpus (16)

• On Quantum Operations as Quantum States
• Channel kets, entangled states, and the location of quantum information
• Density-operator evolution: Complete positivity and the Keldysh real-time expansion
• Balance between quantum Markov semigroups
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• The inverse eigenvalue problem for quantum channels
• Divisible quantum dynamics satisfies temporal Tsirelson's bound
• Norms and Cones in the Theory of Quantum Entanglement
• The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
• Linear-algebraic lambda-calculus
• Maximally genuine multipartite entangled mixed X-states of N-qubits
• Necessary Criteria for Markovian Divisibility of Linear Maps
• Quantum qubit switch: entropy and entanglement
• Entropic characterization of quantum operations
• Entropy of quantum channel in the theory of quantum information
• Divisibility classes of qubit maps and singular Gaussian channels