Infinite-dimensional Hilbert spaces are required in physics to describe systems with continuous degrees of freedom.

the verdict

SUPPORTED

the evidence backs this

Recorded sources

3 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Infinite-dimensional Hilbert spaces are standard mathematical structures used to analyze and describe physical systems possessing continuous degrees of freedom, such as continuous-variable quantum systems and quantum fields.

The analysis

The retrieved literature (e.g., papers 0, 1, and 2) confirms that physical systems with continuous degrees of freedom—such as continuous variables in quantum mechanics and gauge fields—are naturally described using infinite-dimensional Hilbert spaces. None of the papers refute this foundational aspect of quantum theory.

Evidence for · 3

Quantum information processing in phase space: A modular variables approach

Recorded source metadata

A. Ketterer, A. Keller, S. Walborn, T. Coudreau, P. Milman. Quantum information processing in phase space: A modular variables approach. 2015. https://doi.org/10.1103/PhysRevA.94.022325

Discusses how binary quantum information can be encoded using states defined in infinite-dimensional Hilbert spaces to handle continuous degrees of freedom.

Source citation format

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More for · 2

Quantum computation of SU(2) lattice gauge theory with continuous variables

Recorded source metadata

Victor Ale, Nora M. Bauer, Raghav G. Jha, Felix Ringer, G. Siopsis. Quantum computation of SU(2) lattice gauge theory with continuous variables. 2024. https://doi.org/10.1007/JHEP06(2025)084

Uses continuous variables to represent the infinite-dimensional Hilbert space of gauge fields in SU(2) lattice gauge theory.

Source citation format

Bosonic Quantum Computational Complexity

Recorded source metadata

Ulysse Chabaud, M. Joseph, S. Mehraban, Arsalan Motamedi. Bosonic Quantum Computational Complexity. 2024. https://doi.org/10.22331/q-2026-05-20-2110

Lays foundations for quantum complexity theory involving physical systems with continuous degrees of freedom over infinite-dimensional Hilbert spaces.

Source citation format

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first checked01 Aug 2026

judged → SUPPORTED · 8501 Aug 2026

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