Uncertainty Relations and Their Applications

Quantum mechanics has profoundly changed our understanding of the world. The uncertainty principle is viewed as a striking and fundamental feature in quantum mechanics, differing from its classical counterpart. It offers an important lower bound to predict outcomes of arbitrary incompatible observables measured on a particle. With the advent of quantum information science, there gives rise to various methods to express the uncertainty relations, forming the standard deviation uncertainty relations, entropic uncertainty relations, fine-grained uncertainty relation, Majorization entropic uncertainty, in the absence of quantum memory. And, the uncertainty relations explicitly contain bipartite quantum memory uncertainty relations, tripartite quantum memory uncertainty relations, information exclusion principle, etc, with quantum memory. In particular, the uncertainty relations give rise to wide applications in aspects including quantum randomness, quantum teleportation, quantum key distribution, quantum cryptography, quantum steering, entanglement witness, quantum metrology, and so forth.

In this Research Topic, Topic Editors aims to collect articles on the development of various uncertainty relations and their relevance such as quantum resource theories. High-quality Original Research, Review, Mini Review and Perspective articles in these themes are all welcome. Research interests include but are not limited to the following areas:

1. Entropic uncertainty relations
2. Variable-based uncertainty relations
3. fine-grained uncertainty relation
4. Majorization uncertainty relations
5. Coherence uncertainty relations
6. Quantum resource theories and their connection to uncertainty relations
7. Applications of the uncertainty relations in quantum information processing