Quantum Information Theory and Quantum Statistics

By Dénes Petz. 2007

649 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7b276814cf1078d7262764f1acbc2e202c11fc33

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

Citations in the corpus

Quantum channels and memory effects (2012, background): “eral information quantities. In analogy with classical information theory, one denes the quantum mutual information between the reference system R(which mirrors the input Q) and the output system Q0(Petz, 2008), as I(ˆ;) := S(ˆ0 R) + S(ˆ0 Q) S(ˆ0 RQ) = S(ˆ) + S(( ˆ)) S(ˆ;) : (B4) Notice that an impo”
Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference (2011, background): “This fact is known in the quantum probability literature (see [14] example 9.”
Entropy production and the arrow of time (2009, methodology): “In fact, these entropies are used to quantify the degree of entanglement in quantum information theory [27, 28].”
Wireless Myths, Realities, and Futures: From 3G/4G to Optical and Quantum Wireless (2012, background): “The rudiments of classic information-theoretic capacity were highlighted and relied upon in the earlier parts of this treatise, but its generalization to quantum information theory [142] is beyond the scope of this paper.”
Is the Quantum State Real? An Extended Review of -ontology Theorems (2014, background): “Both A and B (H) are examples of von Neumann algebras, and a generalization of classical measure theoretic probability can be developed by defining generalized probability distributions to be positive normalized functionals on such algebras [80, 81].”
Geometry of Quantum States: Index (2007, background): “But these matters [415, 733, 969] are beyond the ken of our book.”
Introduction to Matrix Analysis and Applications (2014, background): “The quantum information application is contained in the same paper and also in the book [68].”
Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints (2015, neutral): “Lemma 1 (Audenaert [3], Petz [32]) For states ρ and σ on a Hilbert space A of dimension d = |A| < ∞, if 12‖ρ− σ‖1 ≤ ǫ ≤ 1, then”
The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, background): “Detailed expositions of the von Neumann entropy can be found in the books by Ohya and Petz [105] and Petz [116].”
Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, methodology): “In the present case involving tensor product of Hilbert spaces, these conditions ask for the state ρ0 to be of a product type ρ0 = ω1 ⊗ ω2 ⊗ ω3, [42], which is not the case for the vacuum of a QFT.”
Quantum Fisher information matrix and multiparameter estimation (2019, background): “Update to date, only known states in single-parameter estimation that own parameter-independent optimal measurement is the so-called quantum exponential family [27,90], which is of the form ρ = e 1 2( ∫ x 0 c(x ′)dx′O− ∫ x 0 x ′′′)ρ0e 1 2 ( ∫ x 0 c(x ′)dx′O− ∫ x 0 x c(x)dx), (114) where c(x) is a fu”
Entanglement Renyi entropies in holographic theories (2010, methodology): “For more details, we refer the reader to the books [10, 11] and the review [12]; the latter provides a comprehensive introduction to Rényi and entanglement entropies in two-dimensional CFTs.”
Introduction to Quantum Fisher Information (2010, background): “…f : R + → R + used here are the standard operator monotone functions deﬁned as These functions are between the arithmetic and harmonic means [27, 44]: Given f , m f ( x, y ) = yf x y is the corresponding mean and we have A necessary condition for the positivity of J is f ( x ) ≤ √ x , while the…”
A Survey on Quantum Channel Capacities (2018, methodology): “The quantum relative entropy function was originally introduced by Umegaki, and later modified versions have been defined by Ohya, Petz and Watanbe [409].”