Quantum Information Theory

By R. Schumann. 2000

556 citations recorded by the source corpus.

In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe. The treatment is pedagogical and suitable for beginning graduates in the field.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/dcce6aac24eb88e323dea6c7975474bf1ae3517b

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In Artificial Intelligence

Citations in the corpus

Inequalities for Trace Norms of 2 × 2 Block Matrices (2003, background): “Such maps describe the evolution of open quantum systems, or quantum systems in the presence of noise [3].”
Causal and localizable quantum operations (2001, background): “To prove this, we first recall that since linear operators are a vector space with a Hilbert-Schmidt inner product, a bipartite operator (whether unitary or not) can be Schmidt decomposed [30].”
Black holes as mirrors: Quantum information in random subsystems (2007, background): “Quantum information theory addresses quantitative questions about the acquisition, transmission, and processing of information in quantum systems [4].”
What is quantum information (2016, background): “Although there were many works on the matter before the article of Benjamin Schumacher (1995) “Quantum Coding” (see, for instance, Ingarden 1976), this work is usually considered the first precise formalization of the quantum information theory.”
Quantum Digital Signatures (2001, unknown): “ar X iv :q ua nt -p h/ 01 05 03 2 v2 15 N ov 2 00 1”
Quantum Information Processing with Finite Resources - Mathematical Foundations (2015, background): “omit proofs. We instead refer to standard textbooks for a more comprehensive treatment. Nielsen and Chuang’s book [111] offers a good introduction to the quantum formalism. Hayashi’s [64] and Wilde’s [155] books both also carefully treat the concepts relevant for quantum information theory in ﬁnite ”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “Despite this, physically relevant states often possess additional structure not found in arbitrary states, and as such do not exhibit this pathological complexity, allowing them to be efficiently described and studied.”
A Survey on Quantum Channel Capacities (2018, background): “In this paper we have not mentioned the definition of unit resource capacity region and private unit resource capacity region, which can be found in detail in the works of Hsieh and Wilde [242], and Wilde and Hsieh [537].”