Related papers: New Quantum Bounds for Inequalities involving Marg…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…
We attempt to pull together various lines of research whose ultimate conclusion points to the actual ``locality'' of Quantum Mechanics (QM). We note that just as John Bell discovered various errors in previous ``proofs'' of the completeness…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Quantum parameter estimation holds significant promise for achieving high precision through the utilization of the most informative measurements. While various lower bounds have been developed to assess the best accuracy for estimates, they…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for the normal and non-normal high-energy approximation of the…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…
In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…
By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative bound for the entropic central limit theorem under the…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
We present a novel tight bound on the quantum violations of the CGLMP inequality in the case of infinitely many outcomes. Like in the case of Tsirelson's inequality the proof of our new inequality does not require any assumptions on the…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a generalization of the method of Calkin and Wilf…
A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)].…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…