MaxEntangled

MaxEntangled
Produces a maximally entangled bipartite pure state
Other toolboxes required	none
Related functions	Bell
Function category	Special states, vectors, and operators

MaxEntangled is a function that returns the canonical maximally entangled bipartite pure state. The state can be chosen to be either full or sparse.

Syntax

• PSI = MaxEntangled(DIM)
• PSI = MaxEntangled(DIM,SP)
• PSI = MaxEntangled(DIM,SP,NRML)

Argument descriptions

• DIM: The dimension of the local subsystems on which PSI lives.
• SP (optional, default 0): A flag (either 1 or 0) indicating that PSI should or should not be sparse.
• NRML (optional, default 1): A flag (either 1 or 0) indicating that PSI should or should not be scaled to have Euclidean norm 1. If NRML=0 then PSI has Euclidean norm sqrt(DIM) and every element of PSI is 0 or 1.

Examples

A maximally entangled qubit state

To generate a maximally entangled pair of qubits you can use the following line of code:

>> MaxEntangled(2)

ans =

    0.7071
         0
         0
    0.7071

If you want an unnormalized version of this state in which each entry of the vector is 0 or 1, specify NRML=0:

>> MaxEntangled(2,0,0)

ans =

     1
     0
     0
     1

In larger systems

When DIM is large, it is usually best to specify SP=1 in order to save memory. For example, this code produces a maximally entangled pure state in $\mathbb{C}^{10} \otimes \mathbb{C}^{10}$:

>> MaxEntangled(10,1)

ans =

   (1,1)       0.3162
  (12,1)       0.3162
  (23,1)       0.3162
  (34,1)       0.3162
  (45,1)       0.3162
  (56,1)       0.3162
  (67,1)       0.3162
  (78,1)       0.3162
  (89,1)       0.3162
 (100,1)       0.3162

Source code

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