 Do vzduh naleko... Do vzduh nekaj vzduh naleko z tem, da je bilo izvizdu,veda, da so inočne vzdušnji, da so inočne vzdušnji. Vzdušnjamo skupnje objezdu. Zelo je z Kadeža, nekaj, nekaj, nekaj, nekaj, nekaj, nekaj. kaj je z jazem v zelo, vseč je z vsečenih mediterranja, z Marokko, da? Tako, da se je tudi tudi, da smo vsečali, da smo vsečenih, zato vseči in vsečenih indikatorov na Markovene in Markovene Danahmi. Kadeža, da se prič. Počke. Počke. So, hej, vseč. Moje njiha je Kadeža Lennos in je z Markovene, Krimelk, Kisati, Universtiv. moročko. Prvo, da, zelo, da bo evoš jaz sem zaštah, da bi pomovil pristiti, da bo srednout mojjo vse svojo, to, da, ta svoja vso je vse turbo, tudi in inkrično, vse, ti, vse, ti, vse. Na srečke, ta srečke, pa je tudi, da, da, ta srečke, pa je tudi, da, to, ta srečke, pa je tudi, pa je tudi, pa je tudi, pa je, ta srečke, pa je tudi, pa je, ta, ta, As we know, today's society is often dabit to a communication society because of the importance of mass media and communication in our lives. Indeed, we can catch information on any topic from anywhere via our computers or even via our smartphones. So the most popular questions arises in the last 2 decades is what is information itself, and second one if we have a random variable ex that theories about probability distribution P. So how much information one can learn from CNX. Of course, the answer to these questions is given to us by information theory introduced by Clodch channel at 1940. So, if we look for an exact definition of information, we merely agree that it is a quantity expressed in bytes. And as I said, the authorship is attributed to Clodch channel at 1940. But along before him, Roland Eilmar Fischer treated the notion of information in his paper at 1922. And he said that it is a way of measuring the amount of information via estimating a parameter of the distribution that model is X. And after 20 years, of course, Clodch channel came with his famous formula, channel entropy, and he said that it is intuitively defines the rate of information, delivered information source as an electrical signal or even for a speed test of 5. However, in the early of 1980, so a group of researchers interested in information theory founded the following scenario. So, if the technological progress being made on the miniaturization of the device, devices used to transmit and process information were to continue, then in the near future we would be able to store information at atomic particle and microscopic scale. So, in this case, quantum scenario for transmission and processing information were to continue and of course leads to what we call quantum information theory as you know. So, one of the important concepts in quantum information theory is often quantum systems. But, let me start with a very brief definition of closed system. So, as we know, a closed system is a system that does not interchange information, which is matter or energy with other external systems. So, of course, the first quantum method describing the dynamics of closed quantum system is given by Schrodinger equation. But, this is not always the case. In general, case in a quantum system can interchange information with other systems and this gives a rise to open quantum systems, where in general this system, open quantum system is connected or is in interaction with its environment. So, now, if we assume that the coupling between the system and its environment is weak and the environment is memoryless, then in this case the dynamics is to be Markovian. If not, if the memory effects between the open quantum system and its environments are always taken into account, then in this case the dynamics is no Markovian and, of course, the reduced density operator for the open quantum system can be evolved in time using, for example, the linear blood master equation. So, another concept known in quantum information theory is what we call quantum speed in its time. So, it is originally known as the minimum evolution time between two distinguishable states and it is given by the maximum between three different quantities, which are given by this formula, where in general this pattern key norm is defined as this formula, where lambda 1 to lambda n are the singular values of this operator. So, in particular, where key is equal to 1, I mean, we are in this situation, then this norm is simply the choice plus norm. If key is equal to 2, then this norm defines the Wilbert Schmidt norm and if key, if we are in this situation, then this norm defines simply the so-called operator norm. However, this quantity describes the birth angle between the initial state and its target. So, another concept we use it in quantum information theory and quantum estimation theory is what we call quantum information theory and it is used to detect the precision of a parameter via estimating some parameters encoded in a quantum state. So, why we use quantum feature information? Because in general and in quantum information theory it isn't always possible to quantify directly parameters encoded in a quantum state. So, for this reason quantum feature information get away to solve this problem via estimating some parameters encoded in a quantum state. So, it is formally based on the symmetry kilogarismic derivative operator and it is given by this formula where epsilon is parameter to be estimated, rho epsilon is the state and L epsilon is the symmetry kilogarismic derivative operator which satisfies this solution. So, now if one can make the special decomposition for the density operator rho epsilon, then the quantum feature information can be written as this form where lambda e and psi e are the eigen values and eigen vectors of this state. And of course, we can also define the quantum feature information for any single cubic system and as we know the density operation for any single cubic system can be defined in terms of its rock vector and Pauli matrices. Then the quantum feature information for any single cubic system is defined as this form. So, based on this we mainly focus our attention to investigate the relation to make a comparative study between quantum speed limit time and quantum feature information actually for three different open quantum systems but I will present just two open quantum systems to examine the Markovianity and or the normal Markovianity of the dynamics of these systems. So, Pauli means start with the first proposed model. So, this model reflects the interaction between a single particle with a set of particles. So, this is the open quantum system and the rest of the particle represents the environment. Of course, the open quantum system is described by this measure equation where each is one is the Hamiltonian the self Hamiltonian of the atom which is given by this formula and the capital here denotes the decoherence rate. So, after some straightforward calculations and for any t greater than zero the reduced density operator of the first open quantum system is given by this formula where d is the decoherence function and it is given by this formula as you see here it depends basically on the time parameter t it depends on the decoherence rate and also it depends on this quantity which represents the difference between the center particle and the other particle. So, the second model is based on the interaction between a single QB system with a non-retronome learning cavity. So, of course, the interaction between these two systems is governed by Jean Skarmin's model and in the 18-wave approximation the total Hamiltonian is given as the sum between Hamiltonian of the atom plus the self Hamiltonian of the electromagnetic field plus the interaction Hamiltonian between these two systems. So, again, after some straightforward calculations and for any t greater than zero the reduced density operator of the second open quantum system is given by this formula where gamma denotes the decoherence function and it can be found in the plus transform the inverse of plus transform the Lorentzian distribution and so on so forth. So, as a result, we have here some analytical results. We have calculated quantum speed limit time for both open quantum systems. So, for example, for the first open quantum system we have calculated quantum speed limit time between the initial stage which is performed as this formula and is targeted and then we have calculated the quantum speed limit time again we have also calculated quantum speed limit time for the second open quantum system of the initial stage which is given by this formula and it's targeted and we have this formula. So, as you see here both quantities depend basically on the decoherence function for each open quantum system. We have also calculated quantum future information and again it is clear that both quantities also depend on the decoherence function of each system. So, here we have some plots we have calculated so, let me start with the first model so, we have plotted the amount of quantum speed limit time and quantum future information again is the parameter delta x so, I remember that delta x is the difference between multiple and the other particles so, we can have some negative equations of course so, we have for the first few here we have plotted the amount of quantum speed limit time so, a remarkable transition from no speed up phenomenon to speed up phenomenon is clearly appeared so, in the first region it is clear that the quantum speed limit time increases but really to reach the minimum value for delta x equal to zero and then increases to reach the maximum value for the particular values of delta x in the plot of quantum future information in the first region it is clear that the amount of quantum future information increases gradually to reach the maximum bound and then decreases fast to completely vanishes at delta x equal to zero and then we have a symmetric behavior in the second region and in general it is clear that for both quantities quantum speed limit time and quantum future information these two quantities increases at the rest of the time also increases so, how can we interpret this phenomenon? phenomena so, in the first region when quantum speed limit time increases and quantum future information decreases and quantum future information increases and then decreases we have interpreted this as so, the open quantum system provides the information to its environment so, at this critical point namely delta x equal to zero the open quantum system provides the maximum of information to its environment however, in the second region when the quantum speed limit time increases and quantum future information increases then we have interpreted this that there is a feedback of information from the environment to its system which means that the open quantum system becomes strongly capital to its environment which make accelerate the speed of the system so, since we have this exchange of information between the open quantum system and its environment in this case the dynamics is said to be long Markovian which is not the case for the second model namely a single qubit interacts with a non-detronomical in cavity so, similarly here we have posted the amount of quantum speed limit time and quantum future information but now again is the coupling with parameter so, it is clear that the quantum speed limit time behaves linearly and speed of phenomenon doesn't occur which means that only the open quantum system gives the information to its environment and there is no feedback of information from the environment to its system which can be also seen from the behavior of quantum future information where as you see here in this point the amount of quantum future information is completely vanished which means that the open system keeps its local information for the remaining values it is clear that the amount of quantum future information increases linearly which means again that only the open system provides the information and there is no feedback of information to the qubit which means that the dynamics is Markovian so, as a summary in the first model it is shown that the quantum speed limit time and quantum future information is looked with similarly between their maximum and minimum bounds we have concluded that the information is transmitted from the open quantum system to its environment and feeds back again to the system whereas for the non-disunely knowledge and cavity the quantum speed velocity limit time and quantum future information are always linear which means that the information flow trained is irreversible and the information cannot feed back to the qubit and then we have concluded that quantum speed limit time and quantum future information can be considered as a good indicator for Markovian or and non-Markovian climate so, I have not enough time to show you all the results we have also added a third quantum open quantum system in order to check our results and we have also added non-Markovianity measurement in order to prove our results and I think we have got an interesting result so, if you are interested you can check our paper and finally I would love to thank my collaborators my previous supervisor Prof. Rahim Galate from Markovian University, Morocco and also my collaborator Prof. Nasser Mithvalli from Markovian University and finally, thank you very much for your effort thank you very much for the talk, for being perfectly in time are there questions from the audience hi, thank you very much for a nice talk I wanted to ask if you could go back to the definition for the quantum speed limit time I wanted to ask you if you can clarify what kind of formula you are using for the speed limit time because I know so, for example, the one that I know is the speed limit time for unitary dynamics for closed system then there are generalization for Linbladian kind of evolution but I guess in this case you are using an even more general speed limit time because it has to be valid so for non Markovian ones so if you could clarify this yes, I agree with you quantum speed limit time first is defined for closed quantum system using the Mandishtam and left hand inequalities but for open quantum system they are used in order to define the quantum speed limit time for open quantum systems and it is given actually by this quantity which is the max between these quantities and we can use it for open quantum system the most important one is that you can use it the reduced density operator the derivative of your density operator and you can calculate these norms using this definition and then you can calculate the quantum speed limit time for any open quantum system ok, so thank you are there other questions? well then if not, let's thank Kadija again and we proceed we proceed to the