The Role of Relative Entropy in Quantum Information Theory
arXiv:quant-ph/0102094 · doi:10.1103/RevModPhys.74.197
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 I will show 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 uniquely 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 speed-up that quantum computers can achieve over their classical counter-parts are outlined using information theoretic arguments. In addition important implications of quantum information theory to thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations including quantum super-dense coding, quantum teleportation, Deutsch's and Grover's algorithms are also included.
40 pages, 11 figures
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Cited by in corpus (533)
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- No-local-broadcasting theorem for non-signalling behaviours and assemblages
- Quantum thermodynamics under continuous monitoring: a general framework
- Detecting Entanglement by Pure Bosonic Extension
- Dephasing-Controlled Particle Transport Devices
- Reasoning about quantum systems at the macroscopic level
- New monotonicity property of the quantum relative entropy
- Some aspects of the interplay between bipartite correlations and quantum channels
- Single-Atom Verification of the Information-Theoretical Bound of Irreversibility at the Quantum Level