Quantum correlations, local interactions and error correction

Vedral, Vlatko; Rippin, M. A.; Plenio, Martin B.

doi:10.1080/09500349708231878

Cited by 12 publications

(19 citation statements)

References 28 publications

(23 reference statements)

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“…Note also that the classical communication from Alice to Bob in step 2 above is crucial because otherwise the protocol would be impossible to execute (there is a deeper reason for this: if we could perform teleportation without classical communication then Alice could send messages to Bob faster than the speed of light, see e.g. Vedral et al (1997c)). …”

Section: B Teleportationmentioning

confidence: 99%

The role of relative entropy in quantum information theory

2002

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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 superdense coding, quantum teleportation, Deutsch's and Grover's algorithms are also included.

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Section: B Teleportationmentioning

confidence: 99%

The role of relative entropy in quantum information theory

2002

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Section: A a Basic Description Of Teleportationmentioning

confidence: 99%

“…Although one can perform entanglement purification acting on a single pair of particles only [7,21,38], it can be shown that there are states that cannot be purified in this way [27]. Therefore we present a scheme that acts on two pairs simultaneously.…”

Section: A Entanglement Purificationmentioning

confidence: 99%

Teleportation, entanglement and thermodynamics in the quantum world

Plenio¹,

Vedral²

1998

Contemporary Physics

295

246

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Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more particles. We will establish the basic properties of entanglement using quantum state teleportation. These principles will then allow us to formulate quantitative measures of entanglement. Finally we will show that the same general principles can also be used to prove seemingly difficult questions regarding entanglement dynamics very easily. This will be used to motivate the hope that we can construct a thermodynamics of entanglement.

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“…Now, the second stage is the occurrence of errors, represented by the operators {E i } which act on the state of the system only, after which we have i E i |ψ c |m |e i Note that at this stage the measurement has not yet been made so that the state of the apparatus is still disentangled from the rest. In general, the states of the environment |e i need not be orthogonal (Vedral et al 1997). If they are orthogonal this leads to a specific form of decoherence which we might call "dephasing" and will be analysed later.…”

Section: Quantum Error Correction As Maxwell's Demonmentioning

confidence: 99%

Landauer's erasure, error correction and entanglement

Vedral

2000

Proc. R. Soc. Lond. A

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Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analyzed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures thereby linking the ''no local increase of entanglement'' principle to the Second Law of thermodynamics.Comment: 11 pages, 1 figure, to appear in The Proceedings of The Royal Societ

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Quantum correlations, local interactions and error correction

Abstract: We consider the effects of local interactions upon quantum mechanically entangled systems. In particular we demonstrate that non-local correla-PACS number(s) 03.65

Cited by 12 publications

References 28 publications

The role of relative entropy in quantum information theory

The role of relative entropy in quantum information theory

Teleportation, entanglement and thermodynamics in the quantum world

Landauer's erasure, error correction and entanglement

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