TraceDistanceCoherence
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| TraceDistanceCoherence | |
| Computes the trace distance of coherence of a quantum state | |
| Other toolboxes required | CVX |
|---|---|
| Related functions | L1NormCoherence RelEntCoherence RobustnessCoherence |
| Function category | Coherence and incoherence |
| Usable within CVX? | no |
TraceDistanceCoherence is a function that computes the trace distance of coherence of a quantum state $\rho$, defined as follows:
\[C_{\text{tr}}(\rho) := \min_{D \in \mathcal{I}}\big\{ \|\rho - D\|_{\text{tr}}\big\},\]
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
- TDC = TraceDistanceCoherence(RHO)
- [TDC,D] = TraceDistanceCoherence(RHO)
Argument descriptions
Input arguments
- RHO: A state (either pure or mixed) to have its trace distance of coherence computed.
Output arguments
- TDC: The trace distance of coherence of RHO.
- D: A vector such that diag(D) is the closest incoherent state to RHO.
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.
>> d = 5;
>> v = ones(d,1)/sqrt(d); % this is a maximally coherent state
>> TraceDistanceCoherence(v)
ans =
1.6000
>> 2 - 2/d
ans =
1.6000Source code
Click here to view this function's source code on github.