Majorization uncertainty relations for mixed quantum states

Abstract

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of $\rho$ and the entries of a unitary matrix $U$ relating both bases. The obtained results can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as uncertainty relation for the sum of conditional entropies.

13 pages, 7 figures

References in corpus (5)

• Formulation of the uncertainty relations in terms of the Renyi entropies
• Improved bounds in entropic uncertainty relations
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Multiple-copy entanglement transformation and entanglement catalysis
• Interconversion of pure Gaussian states using non-Gaussian operations

Cited by in corpus (16)

• The Optimal Uncertainty Relation
• Uncertainty Relations for coarse-grained measurements: an overview
• Quantum Uncertainty Principles for Measurements with Interventions
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Quasi-Fine-Grained Uncertainty Relations
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories
• The Complementary Information Principle of Quantum Mechanics
• Relating entropies of quantum channels
• Flavor-mass majorization uncertainty relations and their links to the mixing matrix
• Strong Majorization Uncertainty Relations: Theory and Experiment
• Experimental investigation of majorization uncertainty relations in the high-dimensional systems
• The Diminished Quantum Uncertainty in Multipartite Entanglement
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• Sequences of lower bounds for entropic uncertainty relations from bistochastic maps