SchmidtRank

SchmidtRank
Computes the Schmidt rank of a bipartite vector
Other toolboxes required	none
Related functions	OperatorSchmidtRank SchmidtDecomposition SchmidtNumber
Function category	Entanglement and separability

SchmidtRank is a function that computes the Schmidt Rank of a bipartite vector. If the vector is full, the Schmidt rank is computed using MATLAB's rank function. If the vector is sparse, the Schmidt rank is computed using the QR decomposition.

Syntax

• RNK = SchmidtRank(VEC)
• RNK = SchmidtRank(VEC,DIM)
• RNK = SchmidtRank(VEC,DIM,TOL)

Argument descriptions

• VEC: A bipartite vector (e.g., a pure quantum state) to have its Schmidt rank computed.
• DIM (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that VEC lives on.
• TOL (optional, default sqrt(length(VEC))*eps(norm(VEC))): The numerical tolerance used when determining if a Schmidt coefficient equals zero or not.

Examples

The following code computes a random state vector in $\mathbb{C}^4 \otimes \mathbb{C}^6$ with Schmidt rank three, and then verifies that its Schmidt rank is indeed 3:

>> SchmidtRank(RandomStateVector([4,6],0,3),[4,6])

ans =

     3

Source code

Click here to view this function's source code on github.