Related papers: Generalised Pinching Inequality
Using the probabilistic language of conditional expectations we reformulate the force matching method for coarse-graining of molecular systems as a projection on spaces of coarse observables. A practical outcome of this probabilistic…
Quantum measurements can be incompatible, i.e., they can fail to be jointly measurable. Recently, a weaker notion of joint-measurability, called partial joint-measurability, was proposed by Masini et al. in [Quantum 8, 1574 (2024)]. In this…
Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…
Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement…
We introduce a type of measurements that generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the…
This paper derives an inequality relating the p-norm of a positive 2 x 2 block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main…
Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general…
In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…
An inequality in quantum mechanics, which does not appear to be well known, is derived by elementary means and shown to be quite useful. The inequality applies to 'all' operators and 'all' pairs of quantum states, including mixed states. It…
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
The Khinchin-Kahane inequality is a fundamental result in the probability literature, with the most general version to date holding in Banach spaces. Motivated by modern settings and applications, we generalize this inequality to arbitrary…
We present a formalization in Isabelle/HOL of quantum projective measurements, a class of measurements involving orthogonal projectors that is frequently used in quantum computing. We also formalize the CHSH inequality, a result that holds…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators…
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is…
We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
The classical Petty projection inequality is an affine isoperimetric inequality which constitutes a cornerstone in the affine geometry of convex bodies. By extending the polar projection body to an inter-dimensional operator, Petty's…