Quantum and classical entropic uncertainty relations
arXiv:1402.1143 · doi:10.1103/PhysRevA.89.042122
Abstract
How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into a classical component, and an intrinsically quantum mechanical component. We show that the total quantum component in a state is never lower or upper bounded by any state-independent quantities, but instead admits "purity-based" lower bounds that generalize entropic formulations such as the Maassen-Uffink relation. These relations reveal a non-trivial interplay between quantum and classical randomness in any finite-dimensional state.
10 pages, 4 figures. Published version
References in corpus (4)
Cited by in corpus (45)
- Entropic Uncertainty Relations and their Applications
- Observable measure of quantum coherence in finite dimensional systems
- The extraction of work from quantum coherence
- Strong Majorization Entropic Uncertainty Relations
- Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
- Tightening the entropic uncertainty bound in the presence of quantum memory
- Quantum-memory-assisted entropic uncertainty relations
- Quantum uncertainty relation using coherence
- Majorization approach to entropic uncertainty relations for coarse-grained observables
- Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations
- Tightening the tripartite quantum memory assisted entropic uncertainty relation
- Entanglement of three-qubit random pure states
- An uncertainty view on complementarity and a complementarity view on uncertainty
- Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds
- Encoding classical information into quantum resources
- Quantitative wave-particle duality relations from the density matrix properties
- Uncertainty, joint uncertainty, and the quantum uncertainty principle
- Majorization entropic uncertainty relations for quantum operations
- Majorization uncertainty relations for mixed quantum states
- Uncertainty Relations for coarse-grained measurements: an overview
- Certainty relations, mutual entanglement and non-displacable manifolds
- Improved quantum entropic uncertainty relations
- Fine-grained uncertainty relations for several quantum measurements
- Quantifying the incompatibility of quantum measurements relative to a basis
- Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
- The role of quantum non-Gaussian distance in entropic uncertainty relation
- Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
- General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases
- Entropic Heisenberg limits and uncertainty relations from the Holevo information bound
- Uncertainty relations for characteristic functions
- Asymmetry and tighter uncertainty relations for Rényi entropies via quantum-classical decompositions of resource measures
- Estimating the Shannon entropy and (un)certainty relations for design-structured POVMs
- Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
- Quantum preparation uncertainty and lack of information
- Unveiling quantum steering by quantum-classical uncertainty complementarity
- Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
- Uncertainty relations from state polynomial optimization
- Distinguishing classically indistinguishable states and channels
- Experimental investigation of quantum uncertainty relations with classical shadows
- Subsystem eigenstate thermalization hypothesis for translation invariant systems
- Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
- Loss of Information in Quantum Guessing Game
- Better Heisenberg limits, coherence bounds, and energy-time tradeoffs via quantum Rényi information
- Classical noise and the structure of minimal uncertainty states
- Quantum speed limit for observables from quantum asymmetry