2020/04/11 by Yunlong Xiao, Kuntal Sengupta, Siren Yang +1
Computer Science · Physics and Astronomy · #Formalism (music) #Noncommutative and Quantum Gravity Theories #Open quantum system #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum algorithm #Quantum operation #Quantum probability #Quantum process #Quantum state #Uncertainty principle #quant-ph
paper · pdf · doi:10.1103/physrevresearch.3.023077
published as Phys. Rev. Research 3, 023077 (2021) · comments are most welcome!
arxiv created 2020/04/11 · openalex created_date 2020/04/17 · openalex publication_date 2021/04/28 · arxiv updated 2021/05/05 · openalex updated_date 2026/08/05
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and quantum mechanics. The physical systems considered in the uncertainty principle are static in nature and described mathematically with a quantum state in a Hilbert space. However, many physical systems are dynamic in nature and described with the formalism of a quantum channel. In this paper, we show that the uncertainty principle can be reformulated to include process measurements that are performed on quantum channels. Since both the preparation of quantum states and the implementation of quantum measurements are themselves special cases of quantum channels, our formalism encapsulates the uncertainty principle in its utmost generality. More specifically, we obtain expressions that generalize the Maassen-Uffink uncertainty relation and the universal uncertainty relations from quantum states to quantum channels.