The role of relative entropy in quantum information theory

2001/02/19 by Vlatko Vedral, V. Vedral · 10 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/revmodphys.74.197

40 pages, 11 figures

arxiv created 2001/02/19 · openalex publication_date 2002/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.

Citations

• The fabric of reality
• Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer
• On Information and Sufficiency
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Strengths and Weaknesses of Quantum Computing
• A continuity property of the entropy density for spin lattice systems
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Universal upper bound on the entropy-to-energy ratio for bounded systems
• Completely positive maps and entropy inequalities
• Separability Criterion for Density Matrices
• Die gegenw�rtige Situation in der Quantenmechanik
• A fast quantum mechanical algorithm for database search
• Thermodynamics and the measure of entanglement
• Quantum Algorithms Revisited
• Completely positive linear maps on complex matrices
• Distinguishability and Accessible Information in Quantum Theory
• Separability of mixed states: necessary and sufficient conditions
• Quantum theory, the Church–Turing principle and the universal quantum computer
• Zur Theorie der linearen und nichtlinearen Integralgleichungen
• Quantifying Entanglement

Cited by

• Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states
• Average entropy of a subsystem from its average Tsallis entropy
• Dynamics of geometric and entropic quantifiers of correlations in open quantum systems
• Two-mode optical state truncation and generation of maximally entangled states in pumped nonlinear couplers
• Classical capacity of quantum channels with memory
• Entanglement in valence-bond-solid states on symmetric graphs
• Strong subadditivity inequality for quantum entropies and four-particle entanglement
• Relative entropy in higher spin holography
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Introduction to Quantum Information Science