Swap

Swap
Swaps two subsystems within a state or operator
Other toolboxes required	opt_args PermuteSystems
Related functions	PermutationOperator SwapOperator

Swap is a function that swaps the position of two subsystems in the space on which a quantum state or operator live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the PermuteSystems function.

Syntax

• SX = Swap(X)
• SX = Swap(X,DIM)
• SX = Swap(X,DIM,SYS)
• SX = Swap(X,DIM,SYS,ROW_ONLY)

Argument descriptions

• X: a vector (e.g., a pure quantum state) or a matrix to have its subsystems permuted
• 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].
• SYS (optional, default [1,2]): a 1-by-2 vector containing the indices of the subsystems to be swapped
• ROW_ONLY (optional, default 0): If set equal to 1, only the rows of X are permuted (this is equivalent to multiplying X on the left by SwapOperator(DIM,SYS)). If equal to 0, both the rows and columns of X are permuted (this is equivalent to multiplying X on both the left and right by the swap operator).

Examples

Please add examples here.