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Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial [PDF]
QuantumThe Haar measure plays a vital role in quantum information, but its study often requires a deep understanding of representation theory, posing a challenge for beginners.
Antonio Anna Mele
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Continuity of the dual Haar measure [PDF]
Comptes Rendus. Mathématique, 2021 Given a continuous field of locally compact groups, we show that the field of the Plancherel weights of their C*-algebras is lower semi-continuous. As a corollary, we obtain that the dual Haar system of a continuous Haar system of a locally compact ...
Renault, Jean
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CoRR, 2019 According to Haar's Theorem, every compact group $G$ admits a unique (regular, right and) left-invariant Borel probability measure $μ_G$. Let the Haar integral (of $G$) denote the functional $\int_G:\mathcal{C}(G)\ni f\mapsto \int f\,dμ_G$ integrating any continuous function $f:G\to\mathbb{R}$ with respect to $μ_G$.
Arno Pauly +2 more
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Profinite Groups with Many Elements of Bounded Order [PDF]
Advances in Group Theory and Applications, 2022 Lévai and Pyber proposed the following as a conjecture: if G is a profinite group such that the set of solutions of the equation x^n = 1 has positive Haar measure, then G has an open subgroup H and an element t such that all elements of the coset tH have
Alireza Abdollahi +1 more
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VARIABLE LEBESGUE ALGEBRA ON A LOCALLY COMPACT GROUP
Проблемы анализа, 2023 For a locally compact group 𝐻 with a left Haar measure, we study the variable Lebesgue algebra L^(p(.))(𝐻) with respect to convolution. We show that if L^(p(.))(𝐻) has a bounded exponent, then it contains a left approximate identity.
P. Saha, B. Hazarika
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Random quantum circuits are approximate unitary $t$-designs in depth $O\left(nt^{5+o(1)}\right)$ [PDF]
Quantum, 2022 The applications of random quantum circuits range from quantum computing and quantum many-body systems to the physics of black holes. Many of these applications are related to the generation of quantum pseudorandomness: Random quantum circuits are known ...
Jonas Haferkamp
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Haar Measure for non-Hausdorff Locally Compact Groups [PDF]
Advances in Group Theory and ApplicationsThe paper describes two possible ways of extending the definition of Haar measure to non-Hausdorff locally compact groups. The first one forces compact sets to be measurable: with this construction, a counterexample to the existence of the Haar measure ...
Lisa Valentini
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Observation of entanglement transition of pseudo-random mixed states
Nature Communications, 2023 It has been predicted that entanglement phase diagrams of Haar-measure random states can show interesting phenomenology, including entanglement phase transitions.
Tong Liu +9 more
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Proceedings of the American Mathematical Society, 2018 To appear in Proceedings of the ...
Adam Przeździecki +2 more
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