Is Hilbert space discrete?

Details Is Hilbert space discrete? Is Hilbert space discrete?

2005-08-06

arxiv.org/abs/hep-th/0508039v1

Phys.Lett. B630 (2005) 68-72

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, revtex, 1 figure

Scientific paper

10.1016/j.physletb.2005.09.084

We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.

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