Majorization entropic uncertainty relations for quantum operations

Abstract

Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an extension of the previous formulation, which deals with submatrices of a unitary matrix relating orthogonal bases in which measurements are performed. Two classes of majorization relations are considered: one related to tensor product of probability vectors and another one related to their direct sum. We explicitly discuss an example of a pair of one-qubit operations, each of them represented by two Kraus operators. In the particular case of quantum maps describing orthogonal measurements the presented formulation reduces to earlier results derived for measurements in orthogonal bases. The presented approach allows us also to bound the entropy characterizing results of a single generalized measurement.

15 pages, two figures. Minor improvements in the version 2

References in corpus (8)

• Heisenberg's Uncertainty Principle
• The uncertainty principle determines the non-locality of quantum mechanics
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Quantum-coherence quantifiers based on the Tsallis relative $\alpha$-entropies
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Rényi generalizations of quantum information measures
• On generalized entropies and information-theoretic Bell inequalities under decoherence
• Complementarity of information sent via different bases

Cited by in corpus (16)

• Entropic Uncertainty Relations and their Applications
• Effects of Hawking radiation on the entropic uncertainty in a Schwarzschild space-time
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Unsharpness of generalized measurement and its effects in entropic uncertainty relations
• Majorization uncertainty relations for mixed quantum states
• Optimal common resource in majorization-based resource theories
• Approximate transformations of bipartite pure-state entanglement from the majorization lattice
• On entropic uncertainty relations in the presence of a minimal length
• Rényi formulation of uncertainty relations for POVMs assigned to a quantum design
• Conditional entropic uncertainty relations for Tsallis entropies
• On entropic uncertainty relations for measurements of energy and its "complement"
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Relating entropies of quantum channels
• Rényi and Tsallis formulations of separability conditions in finite dimensions
• Flavor-mass majorization uncertainty relations and their links to the mixing matrix