Symmetry-resolved entanglement detection using partial transpose moments

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

Restriction of Exponential Sums to Hypersurfaces

We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter $N$, apart from $N^\epsilon $ losses. In a few instances, we manage to remove these losses.

A New Class of Life Distributions Based on Moment Inequalities

In this paper, a new class of life distribution is named new better than renewal used in moment generating function (NBRUmgf). A new test for exponentiality versus NBRUmgf based on moment inequalities is established. Pitman's asymptotic efficiencies, powers and critical values of the new test are calculated to assess the performance of the test. The right censored data is handled also. Finally some applications are applied to the new test.

CONSTRAINT QUALIFICATIONS IN PARTIAL IDENTIFICATION

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian–Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

Universal Barrier Is n-Self-Concordant

This paper shows that the self-concordance parameter of the universal barrier on any n-dimensional proper convex domain is upper bounded by n. This bound is tight and improves the previous O(n) bound by Nesterov and Nemirovski. The key to our main result is a pair of new, sharp moment inequalities for s-concave distributions, which could be of independent interest.

On Decoupling in Banach Spaces

We consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be approximated by a Haar-type expansion in which only the pre-specified conditional distributions appear. Moreover, we show that in our framework a progressive enlargement of the underlying filtration does not affect the decoupling properties (in particular, it does not affect the constants involved). As a special case, we deal with one-sided moment inequalities for decoupled dyadic (i.e., Paley–Walsh) martingales and show that Burkholder–Davis–Gundy-type inequalities for stochastic integrals of X-valued processes can be obtained from decoupling inequalities for X-valued dyadic martingales.