SchmidtDecomposition

SchmidtDecomposition
Computes the Schmidt decomposition of a bipartite vector
Other toolboxes required	opt_args
Related functions	OperatorSchmidtDecomposition SchmidtRank SchmidtNumber

SchmidtDecomposition is a function that computes the Schmidt decomposition of a bipartite vector. The user may specify how many terms in the Schmidt decomposition they wish to be returned.

Syntax

• S = SchmidtDecomposition(VEC)
• S = SchmidtDecomposition(VEC,DIM)
• S = SchmidtDecomposition(VEC,DIM,K)
• [S,U,V] = SchmidtDecomposition(VEC,DIM,K)

Argument descriptions

Input arguments

• VEC: A bipartite vector (e.g., a pure quantum state) to have its Schmidt decomposition 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.
• K (optional, default 0): A flag that determines how many terms in the Schmidt decomposition should be computed. If K = 0 then all terms with non-zero Schmidt coefficients are computed. If K = -1 then all terms (including zero Schmidt coefficients) are computed. If K > 0 then the K terms with largest Schmidt coefficients are computed.

Output arguments

• S: A vector containing the Schmidt coefficients of VEC.
• U (optional): The left Schmidt vectors of VEC.
• V (optional): The right Schmidt vectors of VEC.

Examples

Please add examples here.