Nathaniel at 18:05, 12 January 2016

2016-01-12T18:05:11Z

Nathaniel: Created page with "{{Function |name=RelEntCoherence |desc=Computes the relative entropy of coherence of a quantum state |rel=L1NormCoherence
RobustnessCoherence
TraceDistance..."

2016-01-12T18:04:49Z

Created page with "{{Function |name=RelEntCoherence |desc=Computes the relative entropy of coherence of a quantum state |rel=L1NormCoherence<br />RobustnessCoherence<br />TraceDistance..."

New page

{{Function
|name=RelEntCoherence
|desc=Computes the relative entropy of coherence of a quantum state
|rel=[[L1NormCoherence]]<br />[[RobustnessCoherence]]<br />[[TraceDistanceCoherence]]
|cat=[[List of functions#Coherence_and_incoherence|Coherence and incoherence]]
|upd=January 12, 2016
|cvx=no}}
<tt>'''RelEntCoherence'''</tt> is a [[List of functions|function]] that computes the relative entropy of coherence of a quantum state $\rho$, defined as follows:

: <math>C_{r}(\rho) := -\mathrm{Tr}(\rho(\log_2(\rho) - \log_2(\rho_{\text{diag}}))),</math>

where $\rho_{\text{diag}}$ is the matrix that has the same diagonal as $\rho$ but is zero elsewhere.

==Syntax==
* <tt>REC = RelEntCoherence(RHO)</tt>

==Argument descriptions==
* <tt>RHO</tt>: A state (either pure or mixed) to have its relative entropy of coherence computed.

==Examples==
===Maximally coherent states===
The largest possible value of the relative entropy of coherence on $d$-dimensional states is $\log_2(d)$, and is attained exactly by the "maximally coherent states": pure states whose entries all have the same absolute value.
<syntaxhighlight>
>> d = 5;
>> v = ones(d,1)/sqrt(d); % this is a maximally coherent state
>> RelEntCoherence(v)

ans =

2.3219

>> log(5)/log(2)

ans =

2.3219
</syntaxhighlight>

{{SourceCode|name=RelEntCoherence}}

@@ Line 8: / Line 8: @@
 <tt>'''RelEntCoherence'''</tt> is a [[List of functions|function]] that computes the relative entropy of coherence of a quantum state $\rho$, defined as follows:
-: <math>C_{r}(\rho) := -\mathrm{Tr}(\rho(\log_2(\rho) - \log_2(\rho_{\text{diag}}))),</math>
+: <math>C_{r}(\rho) := -\mathrm{Tr}\big(\rho(\log_2(\rho) - \log_2(\rho_{\text{diag}}))\big),</math>
 where $\rho_{\text{diag}}$ is the matrix that has the same diagonal as $\rho$ but is zero elsewhere.

RelEntCoherence - Revision history

Nathaniel at 18:05, 12 January 2016

Nathaniel: Created page with "{{Function |name=RelEntCoherence |desc=Computes the relative entropy of coherence of a quantum state |rel=L1NormCoherenceRobustnessCoherenceTraceDistance..."

Nathaniel: Created page with "{{Function |name=RelEntCoherence |desc=Computes the relative entropy of coherence of a quantum state |rel=L1NormCoherence
RobustnessCoherence
TraceDistance..."