期刊
REVIEWS OF MODERN PHYSICS
卷 89, 期 1, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/RevModPhys.89.015002
关键词
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资金
- Industry Canada
- Sandia National Laboratories
- NSERC Discovery Grant
- Ontario Research Fund (ORF)
- Swiss National Science Foundation (SNSF)
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center (NFS) [PHY-1125565]
- Gordon and Betty Moore Foundation [GBMF-12500028]
- ARO grant for Research on Quantum Algorithms at the IQIM [W911NF-12-1-0521]
- University of Sydney Postdoctoral Fellowship
- ARC Centre of Excellence for Engineered Quantum Systems (EQUS)
- STW, Netherlands
- ERC Starting Grant QINTERNET
- NWO VIDI grant
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.
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