Nathaniel: requires CVX

2016-01-12T19:05:46Z

requires CVX

Nathaniel: Created page with "{{Function |name=TraceDistanceCoherence |desc=Computes the trace distance of coherence of a quantum state |rel=L1NormCoherence
RelEntCoherence
RobustnessCo..."

2016-01-12T18:50:07Z

Created page with "{{Function |name=TraceDistanceCoherence |desc=Computes the trace distance of coherence of a quantum state |rel=L1NormCoherence<br />RelEntCoherence<br />RobustnessCo..."

New page

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

: <math>C_{\text{tr}}(\rho) := \min_{D \in \mathcal{I}}\big\{ \|\rho - D\|_{\text{tr}}\big\},</math>

where $\mathcal{I}$ is the set of incoherent quantum states (i.e., the set of density matrices that are diagonal in the standard basis).

==Syntax==
* <tt>TDC = TraceDistanceCoherence(RHO)</tt>
* <tt>[TDC,D] = TraceDistanceCoherence(RHO)</tt>

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

===Output arguments===
* <tt>TDC</tt>: The trace distance of coherence of <tt>RHO</tt>.
* <tt>D</tt>: A vector such that <tt>diag(D)</tt> is the closest incoherent state to <tt>RHO</tt>.

==Examples==
===Maximally coherent states===
The largest possible value of the trace distance of coherence on $d$-dimensional states is $2 - 2/d$, 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
>> TraceDistanceCoherence(v)

ans =

1.6000

>> 2 - 2/d

ans =

1.6000
</syntaxhighlight>

{{SourceCode|name=TraceDistanceCoherence}}

@@ Line 2: / Line 2: @@
 |name=TraceDistanceCoherence
 |desc=Computes the trace distance of coherence of a quantum state
 |rel=[[L1NormCoherence]]<br />[[RelEntCoherence]]<br />[[RobustnessCoherence]]
 |cat=[[List of functions#Coherence_and_incoherence|Coherence and incoherence]]

TraceDistanceCoherence - Revision history

Nathaniel: requires CVX

Nathaniel: Created page with "{{Function |name=TraceDistanceCoherence |desc=Computes the trace distance of coherence of a quantum state |rel=L1NormCoherenceRelEntCoherenceRobustnessCo..."

Nathaniel: Created page with "{{Function |name=TraceDistanceCoherence |desc=Computes the trace distance of coherence of a quantum state |rel=L1NormCoherence
RelEntCoherence
RobustnessCo..."