Difference between revisions of "RelEntCoherence"

	RelEntCoherence
	Computes the relative entropy of coherence of a quantum state
Other toolboxes required	none
Related functions	L1NormCoherence; RobustnessCoherence; TraceDistanceCoherence
Function category	Coherence and incoherence
Usable within CVX?	no

Latest revision as of 18:05, 12 January 2016

RelEntCoherence is a function that computes the relative entropy of coherence of a quantum state $\rho$, defined as follows:

\[C_{r}(\rho) := -\mathrm{Tr}\big(\rho(\log_2(\rho) - \log_2(\rho_{\text{diag}}))\big),\]

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

Syntax

REC = RelEntCoherence(RHO)

Argument descriptions

RHO: 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.

>> 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

Source code

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

@@ 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.