Quantum Information Processing with Finite Resources

Tomamichel, Marco

doi:10.1007/978-3-319-21891-5

Cited by 273 publications

(415 citation statements)

References 134 publications

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“…The final step uses the variational formula for the measured relative entropy (see Lemma 2.34). The third statement of the proposition is proven in [165,Section 4.3.3].…”

Section: Chapter 2 Preliminariesmentioning

confidence: 86%

“…They characterize ultimate limits of various operational tasks such as data compression or channel coding [135,137]. In this thesis, we mainly use entropy measures as mathematical objects whose properties are well studied [40,116,165]. We will not discuss the operational relevance of these measures.…”

Section: Entropy Measuresmentioning

confidence: 99%

“…We will not discuss the operational relevance of these measures. The interested reader may consider [76,165,174] for more information. We next define the entropic quantities that are relevant for this thesis.…”

Section: Entropy Measuresmentioning

confidence: 99%

“…[165,Proposition 4.2]) that the joint convexity property (together with the unitary invariance and the submultiplicativity property) implies the data-processing inequality. It thus remains to verify the final statement of the proposition.…”

Section: Chapter 2 Preliminariesmentioning

confidence: 99%

“…Among the most prominent examples are the so-called Rényi relative entropies that are carefully discussed in several textbooks such as, e.g., [165]. In this section, we review a specific member of this family called the minimal Rényi relative entropy that has been introduced in [112,176].…”

Section: Rényi Relative Entropymentioning

confidence: 99%

See 4 more Smart Citations

Approximate Quantum Markov Chains

Sutter

2018

SpringerBriefs in Mathematical Physics

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“…The final step uses the variational formula for the measured relative entropy (see Lemma 2.34). The third statement of the proposition is proven in [165,Section 4.3.3].…”

Section: Chapter 2 Preliminariesmentioning

confidence: 86%

Section: Entropy Measuresmentioning

confidence: 99%

Section: Entropy Measuresmentioning

confidence: 99%

Section: Chapter 2 Preliminariesmentioning

confidence: 99%

Section: Rényi Relative Entropymentioning

confidence: 99%

See 3 more Smart Citations

Approximate Quantum Markov Chains

Sutter

2018

SpringerBriefs in Mathematical Physics

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Quantum Coherence and Intrinsic Randomness

et al. 2019

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The peculiar uncertainty or randomness of quantum measurements stems from quantum coherence, whose information‐theoretic characterization is currently under investigation. The resource theory of coherence investigates interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as a resource for generating intrinsic randomness by measuring a state in the computational basis. It is observed in a previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a correlated party (classical system) about the system measurement outcome. In this work, the result is re‐derived from a quantum point of view, and then the intrinsic randomness is connected to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there do not exist bound coherent states, these two coherence measures—intrinsic randomness quantified by coherence of formation and by relative entropy of coherence—are different. Interestingly, it is shown that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system.

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Quantum Conference Key Agreement: A Review

2020

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Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario.

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Quantum Information Processing with Finite Resources

Cited by 273 publications

References 134 publications

Approximate Quantum Markov Chains

Approximate Quantum Markov Chains

Quantum Coherence and Intrinsic Randomness

Quantum Conference Key Agreement: A Review

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