Is Hilbert space discrete?

Abstract

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.

4 pages, revtex, 1 figure

References in corpus (5)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Strengths and Weaknesses of Quantum Computing
• Quantum gravity and minimum length
• Minimum Length from Quantum Mechanics and Classical General Relativity
• A Computational Model for Quantum Measurement

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