Benjamin Talbot: Change wording "calculate" to "compute"

2024-08-25T21:13:17Z

Change wording "calculate" to "compute"

Benjamin Talbot: Create new page CoherenceRank

2024-08-25T21:11:35Z

Create new page CoherenceRank

New page

{{Function
|name=CoherenceRank
|desc=Calculates the coherence rank of a pure state
|cat=[[List of functions#Coherence_and_incoherence|Coherence and incoherence]]
|upd=August 25, 2024
|v=0.90}}
<tt>'''CoherenceRank'''</tt> is a [[List of functions|function]] that calculates 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<ref name="JMPP22">Ringbauer, Martin and Bromley, Thomas R. and Cianciaruso, Marco and Lami, Ludovico and Lau, W. Y. Sarah and Adesso, Gerardo and White, Andrew G. and Fedrizzi, Alessandro and Piani, Marco. Certification and Quantification of Multilevel Quantum Coherence. American Physical Society, 10.1103/PhysRevX.8.041007, 2018</ref>.

==Syntax==
* <tt>COHRANK = CoherenceRank(V)</tt>
* <tt>COHRANK = CoherenceRank(V, BASIS)</tt>
* <tt>COHRANK = CoherenceRank(V, BASIS, TOL)</tt>

==Argument descriptions==
===Input Arguments===
* <tt>V</tt>: The vector to compute the coherence rank of.
* <tt>BASIS</tt> (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.
* <tt>TOL</tt> (optional, default 1e-10): The numerical tolerance used in the function.

===Output Arguments===
* <tt>COHRANK</tt>: The coherence rank of V with respect to BASIS.

==Example==
The following example shows that the vector
<math>
\begin{bmatrix}
1 \\ 0
\end{bmatrix}
</math>
has a coherence rank of 2 when measured with respect to the basis
<math>
\left \{
\frac{1}{\sqrt{2}}
\begin{bmatrix}
1 \\ 1
\end{bmatrix},
\frac{1}{\sqrt{2}}
\begin{bmatrix}
1 \\ -1
\end{bmatrix}
\right \}
</math>.
This is because the vector
<math>
\begin{bmatrix}
1 \\ 0
\end{bmatrix}
</math>
becomes
<math>
\frac{1}{\sqrt{2}}
\begin{bmatrix}
1 \\ 1
\end{bmatrix}
</math>
when represented in the given basis, which has 2 non-zero entries.
<syntaxhighlight>
>> v = [1; 0];
>> basis = 1/sqrt(2) * [1, 1; 1, -1];
>> CoherenceRank(v, basis)

ans =

2
</syntaxhighlight>

{{SourceCode|name=CoherenceRank}}
==References==
<references />

@@ Line 1: / Line 1: @@
 {{Function
 |name=CoherenceRank
-|desc=Calculates the coherence rank of a pure state
+|desc=Computes the coherence rank of a pure state
 |cat=[[List of functions#Coherence_and_incoherence|Coherence and incoherence]]
 |upd=August 25, 2024
 |v=0.90}}
-<tt>'''CoherenceRank'''</tt> is a [[List of functions|function]] that calculates 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<ref name="JMPP22">Ringbauer, Martin and Bromley, Thomas R. and Cianciaruso, Marco and Lami, Ludovico and Lau, W. Y. Sarah and Adesso, Gerardo and White, Andrew G. and Fedrizzi, Alessandro and Piani, Marco. Certification and Quantification of Multilevel Quantum Coherence. American Physical Society, 10.1103/PhysRevX.8.041007, 2018</ref>.
+<tt>'''CoherenceRank'''</tt> is a [[List of functions|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<ref name="JMPP22">Ringbauer, Martin and Bromley, Thomas R. and Cianciaruso, Marco and Lami, Ludovico and Lau, W. Y. Sarah and Adesso, Gerardo and White, Andrew G. and Fedrizzi, Alessandro and Piani, Marco. Certification and Quantification of Multilevel Quantum Coherence. American Physical Society, 10.1103/PhysRevX.8.041007, 2018</ref>.
 ==Syntax==

CoherenceRank - Revision history

Benjamin Talbot: Change wording "calculate" to "compute"

Benjamin Talbot: Create new page CoherenceRank