CoherenceRank

CoherenceRank
Computes the coherence rank of a pure state
Other toolboxes required	none
Function category	Coherence and incoherence

CoherenceRank is a function that computes the coherence rank of a pure state with respect to a given basis. The coherence rank of a pure state is defined as the number of non-zero entries it contains when it is expressed in the given basis.

Syntax

• COHRANK = CoherenceRank(V)
• COHRANK = CoherenceRank(V, BASIS)
• COHRANK = CoherenceRank(V, BASIS, TOL)

Argument descriptions

Input Arguments

• V: The vector to compute the coherence rank of.
• BASIS (optional, default standard basis): The reference basis for the coherence rank. Assumed to be provided as a unitary matrix whose columns are the basis vectors.
• TOL (optional, default 1e-10): The numerical tolerance used in the function.

Output Arguments

• COHRANK: The coherence rank of V with respect to BASIS.

Example

The following example shows that the vector \( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \) has a coherence rank of 2 when measured with respect to the basis \( \left \{ \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ -1 \end{bmatrix} \right \} \). This is because the vector \( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \) becomes \( \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \end{bmatrix} \) when represented in the given basis, which has 2 non-zero entries.

>> v = [1; 0];
>> basis = 1/sqrt(2) * [1, 1; 1, -1];
>> CoherenceRank(v, basis)


ans =

     2

Source code

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