Higher entropic uncertainty relations for anti-commuting observables
arXiv:0710.1185 · doi:10.1063/1.2943685
Abstract
Uncertainty relations lie at the very core of quantum mechanics, and form the cornerstone of essentially all quantum cryptographic applications. In particular, they play an important role in cryptographic protocols in the bounded-quantum-storage model, where proving the security of all existing protocols ultimately reduces to bounding such relations. Yet, very little is known about such uncertainty relations for more than two measurements. Here, we prove optimal entropic uncertainty relations for anti-commuting binary observables for the Shannon entropy, and nearly optimal relations for the collision entropy. Our results have immediate applications to quantum cryptography.
8 pages revtex, 2 figures, v2: published version but with figures, min-entropy relation added
References in corpus (5)
Cited by in corpus (38)
- Entropic Uncertainty Relations and their Applications
- Entropic uncertainty relations - A survey
- Conclusive quantum steering with superconducting transition edge sensors
- Unconditional security from noisy quantum storage
- Universal Uncertainty Relations
- Correlation complementarity yields Bell monogamy relations
- A min-entropy uncertainty relation for finite size cryptography
- Entropic uncertainty from effective anti-commutators
- Unbounded violation of quantum steering inequalities
- Notes on general SIC-POVMs
- Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
- Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
- The Power of Noisy Fermionic Quantum Computation
- Uncertainty relations for general unitary operators
- Detecting genuine multipartite entanglement of pure states with bipartite correlations
- Quantum to Classical Randomness Extractors
- Experimental Schmidt Decomposition and Entanglement Detection
- Characterizing quantum states via sector lengths
- Uncertainty relations from graph theory
- Using post-measurement information in state discrimination
- Uncertainty and certainty relations for complementary qubit observables in terms of Tsallis' entropies
- A transform of complementary aspects with applications to entropic uncertainty relations
- Bounding the joint numerical range of Pauli strings by graph parameters
- Entropic uncertainty relations and the stabilizer formalism
- Bell monogamy relations in arbitrary qubit networks
- Trade-offs in multi-party Bell inequality violations in qubit networks
- Optimized state independent entanglement detection based on geometrical threshold criterion
- Unified-entropy trade-off relations for a single quantum channel
- A disturbance tradeoff principle for quantum measurements
- Complementarity in atomic (finite-level quantum) systems: an information-theoretic approach
- Uncertainty relations from state polynomial optimization
- Operational measure of incompatibility of noncommuting observables
- Notes on entropic characteristics of quantum channels
- Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
- Entropic uncertainties for joint quantum measurements
- Restrictions on shareability of classical correlations for random multipartite quantum states
- Uncertainty relation for the position of an electron in a uniform magnetic field from quantum estimation theory
- Multiqubit monogamy relations beyond shadow inequalities