648 Hilbert-space dimensionality in a biphoton frequency comb …
2021年3月11日 · We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after...
Hilbert space - Wikipedia
In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.
Quantum transport of high-dimensional spatial information with a ...
2023年12月13日 · Here we demonstrate how a nonlinear parametric process allows for arbitrary high-dimensional state projections in the spatial degree of freedom, where a strong coherent field enhances the...
2021年8月6日 · We experimentally demonstrate a mode-selective quantum frequency converter over a compound spatio-temporal Hilbert space. We show that our method can achieve high-extinction for high-dimensional quantum state tomography by selectively upconverting the signal modes with a mod-ulated and delayed pump.
Quantum space, quantum time, and relativistic quantum …
2021年9月22日 · We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations.
In this thesis, methods for writing spatio-temporal Gaussian process regression as in nite-dimensional Kalman ltering and Rauch{Tung{ Striebel smoothing problems are presented. These scale linearly with respect to the number of time steps as opposed to the cubic scaling of the direct GP solution.
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of “redundancy-constrained
Basis-neutral Hilbert-space analyzers | Scientific Reports - Nature
2017年3月27日 · By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a ‘Hilbert-space analyzer’ capable of projecting optical...
⋆ In quantum mechanics the state of a physical system is represented by a vector in a Hilbert space: a complex vector space with an inner product. The term “Hilbert space” is often reserved for an infinite-dimensional inner product space having the
Phys. Rev. B 101, 174204 (2020) - Localization from Hilbert space ...
2020年5月15日 · We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in arbitrary spatial dimensions.
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