 and recording in progress yes and now I mean it's just okay sorry what I want to say we'll come back to this session of yes of talks before lunch so the first one is from local from a local so Giuliano Chiricco from from from here she sent a CTP will tell us about measurement induced criticality in dissipative you know you can read it from from the title okay so you have 20 minutes and we will you when five minutes okay thank you now okay okay so this work was done in collaboration with with Mikhail Ciccivilli, Marcello del Monte, Rosario Fazzi and Dario Poletti and does this work with the slides to go on or I can send here in any case and yeah okay so just to give an outline I will first present like a brief introduction of measurement induced transition for entanglement in various systems and then I will briefly talk about non-marcovian quantum jumps for many for many body systems and I will present some results on a free fermion model on which we simulated non-marcovian dynamics for entanglement transition okay so the motivation of this work is that in many a lot of many body systems many body quantum systems in quantum optics quantum computing, quantum technologies in general present this competition between coherent evolution and incoherent dynamics of dissipation and basically this competition leads to a lot of new phenomena including new phase and new phase transitions in particular in the literature they have people have identified two main classes of transitions so one is dissipated phase transitions in which you have all the system you look at the steady state and there is a symmetry break in a certain observable of the system for the steady state and the other one is a transition induced by measurements or dissipation in general in the entanglement of the system so the entanglement got different scaling volume law versus error law depending on the strength of the dissipation in particular in this second case people as usually people started studying this in random circuits in which you have a chain of spins and then you have all the system in time and you have a competition between a unit revolution given by these quantum gates which entangled two spins and then you have this brick layer structure and then you have random local measurements which project the state of the system so the unit revolution they increase the entanglement and the random measurement they decrease the entanglement because they collapse the state so there is this competition and depending on the probability of performing a measurement P there is a transition in the scaling law of the entanglement so for example this entanglement is volume low like with the size of the system below a critical probability and then is area law like scales like an area law above this critical probability. Now I just want to say briefly that this the DPT so the CPDF transitions and transitions entanglement have been observed in a system in which they occur at the same time so they're not the same transition they are distinct transitions but they cannot can occur in the same setting so particularly in this recent work we studied a long range system so anything system with a long range interactions which can be tuned by an exponent alpha and depending on the range of interaction we can have a DPT or entanglement transition which is present not only a short range interaction like it was for random circuits but also for long range interactions. Okay so all these works so far have been done for Markovian system so the measurements or dissipation is Markovian I do a measurement at a certain point certain time and it doesn't care when and where I did the other measurements so the question now is what about non-Markovian dynamics so what happens if I perform measurements which are non-Markovian so they remember about the past of the system so are these entanglement transitions robust to non-Markovian in the in the dissipation. Now to address this issue first we have to understand how to deal with non-Markovian dynamics in quantum systems and here I will probably do a little bit of recap of what Gilquipiro said earlier this morning because I just briefly present one method which you you can use to deal with non-Markovian dynamics in a system which is the non-Markovian quantum jumps method and this is what you do is that you start if you start from a limblad equation for the dynamics of the system so here you have this rate of interaction with the environment delta of t and when delta of t is positive then you have a usual Markovian dynamics in which which you can unravel at the level of the quantum states defining some jump operators and then the system undergoes some normal or forward jumps let's say in which the set goes from initial to a final state by applying this operator with a certain probability that depends on the rate. When delta is negative there is non-Markovianity in action so the system retrieves coherences and goes back to the state that it was before performing the last normal jump so essentially a reverse jump cancels the effect of the last forward jump the system underwent and here you can see that the system goes from an initial state to a target state where the initial state is proportional to the jump operator applied to the target state so essentially we are reversing the effect of the of the last jump and the probability as this extra factor here which is the ratio between the average population in the final state versus the average population initial state and this is essential one to record the correct master equation and two I think in my opinion it gives you a measure like that the system is actually non-Markovian because this quantity is here depend on all the trajectories on the history of the system so the non-Markovian is encoded in this fraction here now this method and you can present actually some results about like of this formalism for a two-level system is great for a single atoms where you like you have a limited number of trajectories but for many body systems there is the problem like there are actually many trajectory to to consider and we try to extend this formalism to many body systems in which you have a unit evolution which can mix different states so essentially you're not limited you can jump many times and you can do all the combination of a normal and reverse jump that you can think of but essentially what we did and like here I would probably be not very clear but I just want to give a glimpse of what is happening we can characterize a state by simply the times at which normal jumps that were never reversed occurred so like if we perform a forward jump at time t and then later on we reverse it then we don't care about the jump because it's like it never happened so we only care about the the jump that were never reversed and the state can be written as a series of unit revolutions interspersed with the jump operators at the time specified by the trajectory we we are considering essentially what happens is that the final state so this psi of t here is the sum of many trajectory so for example if we consider a state in which there are no jumps at the end what we can do is actually performing no jumps at all or performing a normal jump and then reversing it later or performing a normal jump and reversing it immediately at a different time or performing normal jump reversing it normal jump reverse jump and so on like we have all these possible combinations so essentially in many body system the probability of having a certain outcome state is very complicated the sum of all of the probabilities like performing all of these trajectories what we saw is that you can actually sum this series in some cases to actually obtain an expression for the probability and particularly focus on the probability of performing no jumps between time t and time t prime so here we are in the continuous limit and so if you consider the where case in which there is no mark we are in the system in which you can only perform normal jumps then this is the the expression that you have so the probability of performing no normal jumps between t and t prime is just exponential of the integral of the positive part of the rate of interaction what we did was that we saw that we can actually sum the infinite series of all the possible trajectories and it's like the the formula is very similar to the Dyson equation for the green function which you normalize the green function with a certain self energy like here we even called the sigma plus this kind of loops here but basically the expression so if we also consider non-marcovianity the probability of performing no jumps at all between t and t prime is renormalized by also the negative part of the rate of interaction and here what we see is that delta plus minus the absolute value of delta so it's just delta so essentially we are increasing the probability of performing no jumps at all because the effect of non-marcovianity is to go back to the to the outcome where we perform no jumps okay so this formalism is nice I hope so but the up the best applications for for this we we still not clear in our mind what is the best system to apply this formalism so if you actually have suggestions or ideas they're very much welcome but now I will go on to the last part of the talk in which we actually did something simpler so we simulated non-marcovian dynamics by using an ancillary system so we coupled our system of interest to an ancillary system which has a marcovian dynamics and these two systems they both have a non-trivial dynamics like the in our case we consider free fermion systems with some hopping parameters on the two chains and then some interchain coupling and then the dynamics the effect of the dc by the dynamics which are measured random measurement on the second chain is experienced by the first chain filtered through the dynamics of the second chain so we go from a marcovian dynamics on the second chain to a dynamics on the first chain which in general will be non-marcovian essentially we are simulating the effect of non-marcovianity by using a coupling to this auxiliary system or a buff if you want and here we are in free fermion you're studying free fermion so we can do everything in terms of correlation matrices and so we can do something like numerically easier but so here the first result so we consider the entanglement entropy of a partition of the first chain so the our system of interest as function of the partition size small l and we plot this as function of l and this quantity will give us an indication or hints whether the system is in volume low or area low phase and what we find is that if we start from small p then this is the entropy behaves linearly or rather like a sine low as function of small l which indicates a volume low in the system but then if we increase the probability so if we want to pick what one which is the extreme case then this entropy saturates to a constant value very quickly with the small l which indicates an area low so in this case we also we retrieve what is what happens in the marcovian case in which there is a transition between volume and area low phase when we increase the probability here is 32 sites for one chain and 32 for the other that's something we are working on but we still don't have because that will be the clear indicator whether it's a volume lower a lot like here this is just an indicator like we want to have a fit in which you have different be like sizes of the system we see clearly volume lower a lot yeah for now we focus actually like we actually kept studying this at fixed size because we saw something like something interesting that if we fix p equal one so the system would like to be in an area low phase always but if we increase t2 to t12 so t2 is the hopping in the second chain t12 is the interchain hopping so if t2 is small then we are in an area low but if we increase t2 then we recover some signs of volume low and the explanation we gave is that when t2 is large essentially the effect of the measurements on the second chain is scrambled before having time to transmit to the to the first chain so the first chain doesn't feel the effect of the measurements because they are scrambled very fast so it's still in a volume low and here we actually did the color color map of a function of t2 and t12 so if you focus only on this part on this log here so I fixed t12 when we increase t2 we go from a dark region which corresponds to a low to a lighter region which corresponds to volume low which is the result we had before and then there is this log like structure which we think is very likely related to the model we are using so we feel like these regions here of volume low are probably due to resonances in the unit dynamics of the system but we're still working on it we have to fully understand it okay so in conclusion what I wanted to tell you in this talk basically was that these entanglement transitions are driven for Markovian system by the composition between dissipation and coherent dynamics and for non-Markovian systems so we tried so usually simulating a numerically sad and we saw that a non-Markovian quantum jumps matter for many by system could be useful but still we don't have clear what the applications are but we did we simulated the non-Markovian dynamics for a free-ferment system using an unsealed system and we saw that there is evidence of entanglement transition for non-Markovian dynamics but we still have to understand what their what is the role of the bad features in this in this behavior in this transition so with this I would like to thank you and I would be happy to take any questions okay thank you very much are there questions from the online audience not and from the physically present mentally I don't know physically present audience I mean if you want sorry thank you for the talk it was very interesting and clear my question was on the slide with the two fermionic chains the drawing the beginning here so even though for the single chain the overall dynamics is no Markovian is it the claim so the second chain the dynamics is Markovian and for the other one yeah for for the first chain so like if you do like in a master in a limbo the question setting if you do or if you trace out the second chain then you will see a dynamics for okay no Markovian but still preserves Gauchanity yes yes yes it still preserves Gauchanity yes so still you encode everything in the correlation matrix and yes yes yes yes so like this the measurements we are actually measuring the number of particles on the second chain and then so you preserve Gauchanity yes thank you maybe I have a quick question myself oh no there is one okay so there is one online what is it I let's see he's asking if I understand correctly the difficulty in no Markovian quantum jumps is that the ensemble is correlated in the sense the single trajectories are not independent how do you solve this problem yeah okay so that there is a good question yes like the thing is I guess like the question is talking about this this thing that the probability of performing a reverse jump is actually actually depends on all the possible trajectories so the point is that if we look just at the probability of performing no jumps then it actually there are actually many simplification in the in the calculations we do that take care of this probability so essentially by looking at the total probability of having a certain outcome with zero jumps or one jump or two jumps and so on we are already writing everything in terms of these quantities here so essentially we are reducing ourselves to solving a question for these quantities here but this method doesn't have a resolution to follow for example a single trajectory so if I want to write the probability of following this trajectory in which I do a forward jump and then a reverse jump at two particular times it's very hard exactly because it depends on all the other trajectories so like by grouping all the all these trajectories together we are actually solving this problem where we're losing resolution on the times when we perform these jumps essentially okay so I think probably will be satisfied this is going to be fine okay so if there are no other questions let's thank him again so