# RelEntCoherence

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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 |

` 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 on "expand" to the right to view the MATLAB source code for this function.