IsProductOperator

IsProductOperator
Determines if an operator is an elementary tensor
Other toolboxes required	opt_args IsProductVector PermuteSystems SchmidtDecomposition
Related functions	OperatorSchmidtDecomposition OperatorSchmidtRank

IsProductOperator is a function that determines if a bipartite or multipartite operator is an elementary tensor or not. If it is an elementary tensor, its tensor decomposition can be provided.

Syntax

• IPO = IsProductOperator(X)
• IPO = IsProductOperator(X,DIM)
• [IPO,DEC] = IsProductOperator(X,DIM)

Argument descriptions

Input arguments

• X: An operator that acts on a bipartite or multipartite Hilbert space.
• DIM (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that X lives on. DIM can be provided in one of three ways:
  • If DIM is a scalar, it is assumed that X lives on the tensor product of two spaces, the first of which has dimension DIM and the second of which has dimension length(X)/DIM.
  • If $X \in M_{n_1} \otimes \cdots \otimes M_{n_p}$ then DIM should be a row vector containing the dimensions (i.e., DIM = [n_1, ..., n_p]).
  • If the subsystems aren't square (i.e., $X \in M_{m_1, n_1} \otimes \cdots \otimes M_{m_p, n_p}$) then DIM should be a matrix with two rows. The first row of DIM should contain the row dimensions of the subsystems (i.e., the m_i's) and its second row should contain the column dimensions (i.e., the n_i's). In other words, you should set DIM = [m_1, ..., m_p; n_1, ..., n_p].

Output arguments

• IPO: Either 1 or 0, indicating that X is or is not an elementary tensor.
• DEC (optional): If IPO = 1 (i.e., X is an elementary tensor), then DEC is a cell containing two or more operators, the tensor product of which is X. If IPO = 0 then DEC is meaningless.

Examples

Please provide some examples.