26 research outputs found
Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
We derive an entropic uncertainty relation for generalized
positive-operator-valued measure (POVM) measurements via a direct-sum
majorization relation using Schur concavity of entropic quantities in a
finite-dimensional Hilbert space. Our approach provides a significant
improvement of the uncertainty bound compared with previous majorization-based
approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111,
230401 (2013); A. E. Rastegin and K. \.Zyczkowski, J. Phys. A, 49, 355301
(2016)], particularly by extending the direct-sum majorization relation first
introduced in [\L. Rudnicki, Z. Pucha{\l}a and K. \.{Z}yczkowski, Phys. Rev. A
89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations
by considering a pair of qubit observables in a two-dimensional system and
randomly chosen unsharp observables in a three-dimensional system. We also
demonstrate that our bound tends to be stronger than the generalized
Maassen--Uffink bound with an increase in the unsharpness effect. Furthermore,
we extend our approach to the case of multiple POVM measurements, thus making
it possible to establish entropic uncertainty relations involving more than two
observables
Robustness measures for quantifying nonlocality
We suggest generalized robustness for quantifying nonlocality and investigate
its properties by comparing it with white-noise and standard robustness
measures. As a result, we show that white-noise robustness does not fulfill
monotonicity under local operation and shared randomness, whereas the other
measures do. To compare the standard and generalized robustness measures, we
introduce the concept of inequivalence, which indicates a reversal in the order
relationship depending on the choice of monotones. From an operational
perspective, the inequivalence of monotones for resourceful objects implies the
absence of free operations that connect them. Applying this concept, we find
that standard and generalized robustness measures are inequivalent between
even- and odd-dimensional cases up to eight dimensions. This is obtained using
randomly performed CGLMP measurement settings in a maximally entangled state.
This study contributes to the resource theory of nonlocality and sheds light on
comparing monotones by using the concept of inequivalence valid for all
resource theories
Fundamental limits on concentrating and preserving tensorized quantum resources
Quantum technology offers great advantages in many applications by exploiting
quantum resources like nonclassicality, coherence, and entanglement. In
practice, an environmental noise unavoidably affects a quantum system and it is
thus an important issue to protect quantum resources from noise. In this work,
we investigate the manipulation of quantum resources possessing the so-called
tensorization property and identify the fundamental limitations on
concentrating and preserving those quantum resources. We show that if a
resource measure satisfies the tensorization property as well as the
monotonicity, it is impossible to concentrate multiple noisy copies into a
single better resource by free operations. Furthermore, we show that quantum
resources cannot be better protected from channel noises by employing
correlated input states on joint channels if the channel output resource
exhibits the tensorization property. We address several practical resource
measures where our theorems apply and manifest their physical meanings in
quantum resource manipulation.Comment: 12 pages, 3 figure