Entropic uncertainty relations and their applications

By Patrick J. Coles, Mario Berta, Marco Tomamichel, Stephanie Wehner. 2015

544 citations recorded by the source corpus.

Heisenberg’s uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the security analysis of almost all quantum cryptographic protocols, such as quantum key distribution and two-party quantum cryptography. This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements. These ideas are then extended to incorporate quantum correlations between the observed object and its environment, allowing for a variety of recent, more general formulations of the uncertainty principle. Finally, various applications are discussed, ranging from entanglement witnessing to wave-particle duality to quantum cryptography.

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

View Paper: https://www.semanticscholar.org/paper/d14c04d9c1d1da0d4a2445f7ba52b58866811202

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Xiongfeng Ma
2. Hoi-Kwong Lo
3. Jian-Wei Pan
4. Feihu Xu
5. Qiang Zhang
6. Otfried Gühne
7. H. C. Nguyen
8. Roope Uola

In Atomic and Molecular Physics, and Optics

1. Xiongfeng Ma
2. Jian-Wei Pan
3. Feihu Xu
4. Hoi-Kwong Lo
5. Qiang Zhang
6. Otfried Gühne
7. H. C. Nguyen
8. Roope Uola

Citations in the corpus

• Quantum steering (2019, background): “This and similar EURs are central to quantum information theory and quantum cryptography (Coles et al., 2017).”
• Secure quantum key distribution with realistic devices (2020, methodology): “Nonetheless, the security analysis can be extended to the case of coherent attack by further analysis (Coles et al., 2017; Tomamichel et al., 2012), such as the de Finetti theorem (Renner, 2007), the post-selection technique (Christandl et al., 2009) and uncertainty relation for smooth entropies…”
• Advances in quantum cryptography (2019, unknown): “For the sake of self-consistency, we briefly recall the entropic uncertainty relations (EURs) [505, 680], already discussed in Section IX but here adapted to the notation of the present problem.”