Toric Geometry and String Theory Descriptions of Qudit Systems

Understand

In this paper, we propose a new way to approach qudit systems using toric geometry and related topics including the local mirror symmetry used in the string theory compactification.

• We refer to such systems as (n,d) quantum systems where $n$ and $d$ denote the number of the qudits and the basis states respectively.
• Concretely, we first relate the (n,d) quantum systems to the holomorphic sections of line bundles on n dimensional projective spaces CP^{n} with degree n(d-1).
• These sections are in one-to-one correspondence with d^n integral points on a n-dimensional simplex.