Paper: hep-th/0508039
From: Stephen D. H. Hsu
Date: Sat, 6 Aug 2005 03:15:50 GMT (21kb)
Title: Is Hilbert space discrete?
Authors: R. Buniy, S. Hsu and A. Zee
Comments: 4 pages, revtex, 1 figure
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.
Figure 1: A possible discretization of the Bloch sphere (qubit Hilbert space). Points on each disc (of size $\epsilon$) are identified. Points between discs can be assigned to the nearest disc.
