Zak transform and non-uniqueness in an extension of Pauli's phase retrieval problem

DOI10.1007/s10476-016-0301-zzbMath1389.42008arXiv1501.03905OpenAlexW2964200892MaRDI QIDQ1677562

Simon Andréys, Philippe Jaming

Publication date: 10 November 2017

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.03905

zbMATH Keywords

Zak transformPauli problemFractional Fourier transformPhase retrievalWeyl-Heisenberg transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (3)

Phase Retrieval: Uniqueness and Stability ⋮ On uniqueness properties of solutions of the Toda and Kac-van Moerbeke hierarchies ⋮ Weighted Zak transforms and the dual tiling condition

Uses Software

• PhaseLift

Cites Work

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• On the Pauli problem
• Uniqueness results in an extension of Pauli's phase retrieval problem
• The Pauli problem, state reconstruction and quantum-real numbers
• Phase retrieval techniques for radar ambiguity problems
• Nonuniqueness of phase retrieval for three fractional Fourier transforms
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• The Zak transform and some counterexamples in time-frequency analysis
• Are wave functions uniquely determined by their position and momentum distributions?
• Phase Retrieval via Matrix Completion

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