The role of relative entropy in quantum information theory

By Vlatko Vedral. 2001

950 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/100c17e0f7696662ef825a5e61aaf8abd9a8c845

How researchers see this paper

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In Artificial Intelligence

1. R. Myers
2. T. Nishioka
3. Rosario Fazio
4. H. Casini
5. Luigi Amico
6. A. Osterloh
7. M. Huerta
8. Sándor Imre

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. T. Nishioka
3. Thomas Hartman
4. D. Harlow
5. H. Casini
6. T. Takayanagi
7. T. Faulkner
8. M. Huerta

Citations in the corpus

• Quantum processes which do not use coherence (2015, background): “It is well known [48] that the mutual information I(A ∶ B) is both a deterministic and an ensemble monotone under local operations on either A or B.”
• Coherence effects in the performance of the quantum Otto heat engine (2018, neutral): “[66] V.”
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions (2016, background): “Furthermore, it is important to mention that the action of any Kraus map Φ can never increase the relative entropy [44,46], i.”
• Remarks on the entanglement entropy for disconnected regions (2008, background): “Unfortunately, this does not hold in general, and both signs are allowed [15].”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “It has an interpretation in terms of hypothesis testing [199], but its main use so far has been in proving other statements that are more immediately interesting.”
• Fundamental limits of repeaterless quantum communications (2015, neutral): “This is exactly the case of the REE, for which we may write ER(ρ n ab ) ≤ nER(ρE).”
• A Survey on Quantum Channel Capacities (2018, methodology): “cations of quantum relative entropy in quantum information processing were introduced by Vedral [508].”
• Colloquium: Quantum fluctuation relations: Foundations and applications (2010, background): “, 2009) has established a connection between the topical fields of quantum information theory (Vedral, 2002) and quantum fluctuation relations.”
• Geometry of Quantum States: Index (2007, background): “A general reference for this section is Ohya and Petz [699]; for valuable reviews see Schumacher and Westmoreland [811], and Vedral [917].”
• Relative entropy and holography (2013, neutral): “, [27, 28]).”
• Entanglement entropy: Holography and renormalization group (2018, background): “(38) 9 It measures the “distance” between the two states with several (defining) properties (Ohya, 2004; Vedral, 2002), S(ρ||ρ) = 0 , (39) S(ρ1 ⊗ ρ2||σ1 ⊗ σ2) = S(ρ1||σ1) + S(ρ2||σ2) , (40) S(ρ||σ) ≥ 1 2 ||ρ− σ||2 , (41) S(ρ|σ) ≥ S(trp ρ|trp σ) , (42) where the trp is a partial trace with respect…”