Continuous Approach to Phase (Norm) Retrieval Frames

• URL: http://arxiv.org/abs/2501.08927v1
• Date: Wed, 15 Jan 2025 16:30:45 GMT
• Title: Continuous Approach to Phase (Norm) Retrieval Frames
• Abstract summary: We introduce the concept of continuous near-Riesz bases and prove their invariance under invertible operators.<n>Some equivalent conditions for phase and norm retrieval property of continuous frames are presented.<n>We study the stability of phase retrieval under perturbations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance under invertible operators. Some equivalent conditions for phase and norm retrieval property of continuous frames are presented. We study the stability of phase retrieval under perturbations. Furthermore, tensor product frames for separable Hilbert spaces are studied, and we establish the equivalence of phase retrieval and norm retrieval properties between components and their tensor products.

Related papers

• Phase Retrievability of Super Operators and Measurements [0.0]
  We consider states (and positive semidefinite operators) of bounded rank, as is done in Quantum Tomography.<n>We show that in order to have phase retrieval with respect to positive semidefinite operators of bounded rank, it suffices to discriminate between perfectly distinguishable pairs.
  arXiv  Detail & Related papers  (2026-07-29T04:59:09Z)
• Phase Structure in Rotary Attention: A Spectral Framework for Semantic Continuity and Execution-Boundary Governance [0.0]
  This paper develops a bounded spectral framework for examining rotary phase alignment, hidden-state continuity, and semantic drift.<n>It first identifies ordered hidden-state sequences, rather than vocabulary indices, as valid domains for spectral decomposition.<n>It then derives the Rotary Position Embedding (RoPE) attention score as a sum of magnitude-weighted cosine terms and proves a local stability lemma.
  arXiv  Detail & Related papers  (2026-07-28T09:41:05Z)
• Entropic Uncertainty Relations for Mutually Unbiased Operator Frames [1.7188280334580195]
  We develop an operator-frame formulation of entropic uncertainty relations in the Hilbert-Schmidt space of operators.<n>For general continuous indexed operator frames, we derive an entropic uncertainty relation for the associated coefficient distributions.
  arXiv  Detail & Related papers  (2026-06-22T11:30:18Z)
• Exactly Solvable RD Model: RG Cycles Meet Fractality [45.88028371034407]
  We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking.<n>By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector.<n>We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states.
  arXiv  Detail & Related papers  (2026-03-18T12:54:21Z)
• Persistent Homology via Finite Topological Spaces [0.0]
  We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets.<n>We show that standard poset-level simplifications preserve persistent invariants and prove stability of the resulting persistence diagrams under perturbations of the input metric in a density-based instantiation.
  arXiv  Detail & Related papers  (2025-12-29T10:14:56Z)
• Phase Transitions in Nonreciprocal Driven-Dissipative Condensates [0.6291443816903801]
  We investigate the influence of boundaries and spatial nonreciprocity on nonequilibrium driven-dissipative phase transitions. Our model avoids post-selection or unphysical non-Hermitian Hamiltonians and is experimentally realizable in platforms such as superconducting circuits.
  arXiv  Detail & Related papers  (2025-02-07T19:00:07Z)
• Probing quantum floating phases in Rydberg atom arrays [61.242961328078245]
  We experimentally observe the emergence of the quantum floating phase in 92 neutral-atom qubits. The site-resolved measurement reveals the formation of domain walls within the commensurate ordered phase. As the experimental system sizes increase, we show that the wave vectors approach a continuum of values incommensurate with the lattice.
  arXiv  Detail & Related papers  (2024-01-16T03:26:36Z)
• Defining stable phases of open quantum systems [0.0]
  We show that uniformity is satisfied in a canonical classical cellular automaton. We conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability.
  arXiv  Detail & Related papers  (2023-08-28T17:55:31Z)
• Unified framework for continuity of sandwiched Rényi divergences [0.0]
  We prove continuity bounds for entropic quantities related to sandwiched R'enyi divergences.<n>In a separate contribution, we use the ALAFF method to study the stability of approximate quantum Markov chains.
  arXiv  Detail & Related papers  (2023-08-23T21:09:54Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces [52.424621227687894]
  We introduce a unified framework for group equivariant networks on homogeneous spaces. We take advantage of the sparsity of Fourier coefficients of the lifted feature fields. We show that other methods treating features as the Fourier coefficients in the stabilizer subgroup are special cases of our activation.
  arXiv  Detail & Related papers  (2022-06-16T17:59:01Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)
• Construction and Monte Carlo estimation of wavelet frames generated by a reproducing kernel [14.207723862182947]
  We introduce a construction of multiscale tight frames on general domains. We extend classical wavelets as well as generalized wavelets on non-Euclidean structures. We show that a sample frame tends to its population counterpart, and derive explicit finite-sample rates on spaces of Sobolev and Besov regularity.
  arXiv  Detail & Related papers  (2020-06-17T13:51:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.