Update README.md

Author: brzepkowski

README.md

@@ -356,7 +356,7 @@ autoencoders* [Rochetto et, al. 2018](https://www.nature.com/articles/s41534-018
 
 We examined two kinds of entropy - the von Neumann (entanglement) entropy and Shannon entropy of the output vector (treated as a quantum state-vector) returned by different ML models. It's worth noticing, that these two values are the same, when we express the (quantum) state vector in the Schmidt basis (which can be obtained by means of the SVD). See [here](https://physics.stackexchange.com/questions/600120/von-neumann-entropy-vs-shannon-entropy-for-a-quantum-state-vector/608071#608071) for more details. However, the SVD is never conducted when training ML models, which justifies the different behaviour of the curves presented in above plots. However, we were not able to find any obvious relations between these two entropies, and also between them and the reward obtained by the agent.
 
-We can see that in the case of a classical model trying to reproduce the behaviour of a quantum model the two analyzed entropies differ from the one obtained from a truly quantum model. The two values oscillate around simmilar levels, but the classical model seems to be much more stable.
+We can see that in the case of a classical model trying to reproduce the behavior of a quantum model the two analyzed entropies differ from the one obtained from a truly quantum model. The two values begin their oscillations at a similar level, but for the classical model the entanglement entropy seems to be dropping faster. Also, classical model seems to be "more stable". However, these conclusions shouldn't be regarded as general rules, because in theory other agents might give a different behavior.
 
 Finally, **we suggest, that the von Neumann entropy can be also used during the training of any (classical) ML model**, which outputs a vector of length $4^n$, for some integer $n$. In that case we would just treat the output as the state vector of some quantum system. **The maximization of entropy is widely used in RL by adding it as a bonus component to the loss function (as described [here](https://awjuliani.medium.com/maximum-entropy-policies-in-reinforcement-learning-everyday-life-f5a1cc18d32d) and [here](https://towardsdatascience.com/entropy-regularization-in-reinforcement-learning-a6fa6d7598df)), so it would be interesting to see, if we could gain some different behaviour of an agent by utilizing the entanglement entropy in a similar way**. It should be possible, because the von Neumann entropy is differentiable (see [here](https://math.stackexchange.com/questions/3123031/derivative-of-the-von-neumann-entropy), [here](https://math.stackexchange.com/questions/2877997/derivative-of-von-neumann-entropy) and [here](https://quantumcomputing.stackexchange.com/questions/22263/how-to-compute-derivatives-of-partial-traces-of-the-form-frac-partial-operat)).