Quantum computation and quantum information
Quantum computation and quantum information
Rényi Extrapolation of Shannon Entropy
Open Systems & Information Dynamics
Geometry of Quantum States: An Introduction to Quantum Entanglement
Geometry of Quantum States: An Introduction to Quantum Entanglement
A tight high-order entropic quantum uncertainty relation with applications
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Limits on entropic uncertainty relations for 3 and more MUBs
Quantum Information & Computation
Relaxed uncertainty relations and information processing
Quantum Information & Computation
Quantum Information Processing
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Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in both the state-dependent and state-independent forms. A few examples are discussed as well. Using the Pegg-Barnett formalism and the Riesz theorem, we obtain a nontrivial inequality between norm-like functionals of generated probability distributions in finite dimensions. The principal point is that we take the infinite-dimensional limit right for this inequality. Hence number-phase uncertainty relations with finite phase resolutions are expressed in terms of the unified entropies. Especially important case of multiphoton coherent states is separately considered. We also give some entropic bounds in which the corresponding integrals of probability density functions are involved.