# Coherence measurement for density matrix

I have a density matrix of the form:

$$\rho(t)=\left[ \begin{array}{ccc} \frac{1}{4}+\frac{1}{12} e^{-\frac{2 \tau ^{2 H+2}}{2 H+2}} & \frac{1}{3} & \frac{1}{4}+\frac{1}{12} e^{-\frac{2 \tau ^{2 H+2}}{2 H+2}} \\ \frac{1}{3} & \frac{1}{2}-\frac{1}{6} e^{-\frac{2 \tau ^{2 H+2}}{2 H+2}} & \frac{1}{3} \\ \frac{1}{4}+\frac{1}{12} e^{-\frac{2 \tau ^{2 H+2}}{2 H+2}} & \frac{1}{3} & \frac{1}{4}+\frac{1}{12} e^{-\frac{2 \tau ^{2 H+2}}{2 H+2}} \\ \end{array} \right].$$

I want to quantify/observe the time evolution of coherence for this matrix showing dynamics of a quantum system between any two times $$\tau_o$$ and $$\tau$$ except using entropies. I will be thankful for your time and kind help.

• What do you mean by “compute coherence”? Sep 23, 2021 at 18:55
• @Mauricio, This is a matrix showing dynamics of a quantum system. Thus, I am interested in to find the coherence value in the matrix at t=0 and at any other time t. As entanglement is measure by the concurrence or any other measure. Sep 24, 2021 at 6:23
• This review paper list a lot of coherence measure. And I think you can start from a relatively easy one:$l_1$ norm-based coherence measure, i.e., $\sum_{i\neq j}|\rho_{ij}|$(eq.(38) in the link paper). Sep 24, 2021 at 7:40
• I don't understand. Are you looking to the entanglement, or the coherences? You want to compute the relative entropy of what exactly? And how do you define/quantify "coherence" here? And what issues precisely are you having in doing this?
– glS
Sep 24, 2021 at 12:43
• @Attakhan what do you mean by "coherence value"? Do you have a formula? that would be useful to answer the question. Sep 24, 2021 at 14:43