Related papers: Hierarchy of inequalities for quantitative duality
In this communication, based on our paper http://arxiv.org/abs/1409.4186, we discuss a way of enhancing Gauge/Gravity Duality and response of a dual strongly coupled medium on placing the inhomogeneity on the gravity side.
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
Quantum metrology deals with improving the resolution of instruments that are otherwise limited by shot noise and it is therefore a promising avenue for enabling scientific breakthroughs. The advantage can be even more striking when quantum…
Based on the generators of $SU(n)$ we present inequalities for detecting quantum entanglement for $2 \otimes d$ and $M \otimes N$ systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give…
Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for…
A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as "Hefei inequality" in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed…
We comment on one of the earliest derivations of the so-called wave-particle duality relation. Our aim is to point out a slight technical flaw in the proof, fixing it. Neither the physical content of the duality relation nor its validity is…
With the rapid development of quantum technologies in recent years, the need for high sensitivity measuring techniques has become a key issue. In particular, optical sensors based on quantum states of light have proven to be optimal…
Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…
Optical interferometric imaging enables astronomical observation at extremely high angular resolution. The necessary optical information for imaging, such as the optical path differences and visibilities, is easy to extract from fringes…
We consider the situation when the signal propagating through each arm of an interferometer has a complicated multi-mode structure. We find the relation between the particle-entanglement and the possibility to surpass the shot-noise limit…
Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…
A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…
Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
In this paper, we establish several new inequalities for some twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.