Difference between revisions of "SchmidtDecomposition"

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

Revision as of 23:05, 1 December 2012

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.

@@ Line 4: / Line 4: @@
 |req=[[opt_args]]
 |rel=[[IsProductVector]]<br />[[OperatorSchmidtDecomposition]]<br />[[SchmidtRank]]<br />[[SchmidtNumber]]
-|upd=November 23, 2012
+|upd=December 1, 2012
-|v=1.01}}
+|v=1.02}}
 <tt>'''SchmidtDecomposition'''</tt> is a [[List of functions|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.