Entropic uncertainty relations and their applications

Entropic uncertainty relations and their applications

Coles, Patrick J. (University of Waterloo)
Berta, Mario (California Institute of Technology)
Tomamichel, Marco (University of Sydney)
Wehner, S.D.C. (TU Delft Quantum Internet Division; TU Delft Quantum Information and Software; TU Delft QuTech Advanced Research Centre)

Quantum Internet Division

2017

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.

http://resolver.tudelft.nl/uuid:14442e46-7ede-42de-8c44-a0002a7eb9e3

https://doi.org/10.1103/RevModPhys.89.015002

0034-6861

Reviews of Modern Physics, 89 (1)

Institutional Repository

journal article

© 2017 Patrick J. Coles, Mario Berta, Marco Tomamichel, S.D.C. Wehner