arXiv subjects

Robert Salzmann

Publications and source records attributed to Robert Salzmann.

22 records · Page 2Linked to original sources

arXiv2021

The $α\to 1$ Limit of the Sharp Quantum Rényi Divergence

Fawzi and Fawzi recently defined the sharp Rényi divergence, $D_α^\#$, for $α\in (1, \infty)$, as an additional quantum Rényi divergence with nice mathematical properties and applications in quantum channel discrimination and quantum communication. One of their open questions was the limit $α \to 1$ of this divergence. By finding a new expression of the sharp divergence in terms of a minimization of the geometric Rényi divergence, we show that this limit is equal to the Belavkin-Staszewski relative entropy. Analogous minimizations of arbitrary generalized divergences lead to a new family of generalized divergences that we call kringel divergences, and for which we prove various properties including the data-processing inequality.

quant-ph↗

arXiv2020

Quantum Zeno effect for open quantum systems

We prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.

quant-ph↗

arXiv2019

Derivation of 3D energy-critical nonlinear Schrödinger equation and Bogoliubov excitations for Bose gases

We derive the 3D quintic NLS as the mean field limit of a Bose gas with three-body interactions. The quintic NLS is energy-critical, leading to several new difficulties in comparison with the cubic NLS which emerges from Bose gases with pair-interactions. Our method is based on Bogoliubov's approximation, which also provides the information on the fluctuations around the condensate in terms of a norm approximation for the N-body wave function.

math-ph↗

arXiv2019

Efficient Learning for Deep Quantum Neural Networks

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

quant-ph↗