MinUPBSize

MinUPBSize is a function that returns that minimum numbers of vectors required in an unextendible product basis (UPB), given the dimensions of the local Hilbert spaces. If the minimum size of a UPB in the given space is not known, and error will be produced.

Syntax

 * S = MinUPBSize(DIM)
 * S = MinUPBSize(DIM,VERBOSE)

Argument descriptions

 * DIM: A vector that specifies the local Hilbert space dimensions.
 * VERBOSE (optional, default 1): A flag (either 1 or 0) indicating that a reference to a journal article that provides a proof of the minimal size claimed by this script will or will not be displayed.

Examples
The following code tells the user that the smallest UPB in $$\mathbb{C}^5 \otimes \mathbb{C}^6$$ has $$10$$ states, and points to the reference for a proof of this fact:

The following code gives the same information, but without displaying the reference:

The minimum size of UPBs is also known in many multipartite cases:

Unfortunately, there are also many cases where the minimum size of a UPB is not currently known. In these cases, and error is returned: