We are happy to announce that our work "Gillespie algorithm for quantum jump trajectories" has just been published in Physical Review A.

The jump unraveling of a quantum master equation decomposes the dynamics of an open quantum system
into abrupt jumps, interspersed by periods of coherent dynamics when no jumps occur. Such open quantum
systems are ubiquitous in quantum optics and mesoscopic physics, hence the need for efficient techniques for
their stochastic simulation. Numerical simulation techniques fall into two main categories. The first splits the
evolution into small time steps and determines stochastically for each step if a jump occurs or not. The second,
known as Monte Carlo wave-function simulation, is based on the reduction of the norm of an initially pure
state in the conditional no-jump evolution. It exploits the fact that the purity of the state is preserved by the
finest unraveling of the master equation. In this paper, we present an alternative method for the simulation of
the quantum jump unraveling, inspired by the classical Gillespie algorithm. The method is particularly well
suited for situations in which a large number of trajectories is required for relatively small systems. It allows
for non-purity-preserving dynamics, such as the ones generated by partial monitoring and channel merging. We
describe the algorithm in detail and discuss relevant limiting cases. To illustrate it, we include four example
applications of increasing physical complexity and discuss the performance of the algorithm across regimes of
interest for open quantum systems simulation. Publicly available implementations of our code are provided in
JULIA and MATHEMATICA.

Have a look on Physical Review A here!

We are very excited to announce this work, in collaboration with Dr. Saulo V. Moreira and Prof. Mark T. Mitchison, both at Trinity College Dublin!

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these classical bounds in open quantum systems, motivating the derivation of new quantum TURs and KURs that account for the role of quantum coherence. Here, we go one step further by deriving multidimensional KUR and TUR for multiple observables in open quantum systems undergoing Markovian dynamics. Our derivation exploits a multi-parameter metrology approach, in which the Fisher information matrix plays a central role. Crucially, our bounds are tighter than previously derived quantum TURs and KURs for single observables, precisely because they incorporate correlations between multiple observables. We also find an intriguing quantum signature of correlations that is captured by the off-diagonal element of the Fisher information matrix, which vanishes for classical stochastic dynamics. By considering two examples, namely a coherently driven qubit system and the three-level maser, we demonstrate that the multidimensional quantum KUR bound can even be saturated when the observables are perfectly correlated.

Have a look here!

We are excited to announce that, after the successful conclusion of his Master's project in our group, Yutong Luo now joins the Trinity Quantum Information Theory group as a PhD researcher, funded by the China Scholarship Council.

Yutong will be working on quantum resource theories, focusing specifically on thermodynamics. In particular, he would like to understand how general multi-time quantum processes are constrained by thermodynamic resources, e.g. the equilibrium free energy. He is also interested in the general framework of resource theories of general quantum resources.

Welcome back Yutong, and best of luck for your PhD!

We are proud to announce that the work by our Simon Milz and Marco Túlio Quintino (Sorbonne Université, France) has just been published in Quantum.

We are excited to be hosting the Emergence of Classicality 2024 Conference in Dublin 15-19 July!

For more info, have a look at the conference website here!

The Teaching Assistance activity of group member Marco Radaelli, PhD student in the School of Physics, has been recognised with the School of Physics Teaching Award for the academic year 2023/24. Marco will also be nominated by the School as a candidate for the college-wide Postgraduate Teaching Awards later this year.

Well done Marco!

We are excited to announce that the group has four new members:

Dillon Broaders, MSc student in Quantum Science and Technology at Trinity, is going to research the application of the Petz recovery map for quantum processes with memory.

Jimí Ó Baoill de Faoite, MSc student in Quantum Science and Technology at Trinity, is going to work on efficient approximations to stochastic process models.

Srivathsan Srinivasan, MSc student in Quantum Science and Technology at Trinity, is researching in objectivity theory.

Sean Alexander, BA student in Physics at Trinity, is also going to work on objectivity theory.

We wish them all the best of luck, and we hope they will have a nice and productive time in our group!

We would like to congratulate Marco Radaelli, PhD researcher in the group, for winning a runner-up prize for the competition, held during the Tercentenary of the School of Physics celebrations. The competition saw the participation of a number of PhD students from different research groups in the School. We also would like to congratulate Lórien MacEnulty and Cian O'Toole for being awarded, respectively, the first place and the other runner-up prize!

Have a look at the new preprint by group member Dr. Alessandro Candeloro, with Zahra Pazhotan and Matteo G.A. Paris (both University of Milan)!

We study the role of probe dimension in determining the bounds of precision and the level of incompatibility in multi-parameter quantum estimation problems. In particular, we focus on the paradigmatic case of unitary encoding generated by SU(2) and compare precision and incompatibility in the estimation of the same parameters across representations of different dimensions. For two- and three-parameter unitary models, we prove that if the dimension of the probe is smaller than the number of parameters, then simultaneous estimation is not possible (the quantum Fisher matrix is singular). If the dimension is equal to the number of parameters, estimation is possible but the model exhibits maximal (asymptotic) incompatibility. However, for larger dimensions, there is always a state for which the incompatibility vanishes, and the symmetric Cramér-Rao bound is achievable. We also critically examine the performance of the so-called asymptotic incompatibility (AI) in characterizing the difference between the Holevo-Cramér-Rao bound and the Symmetric Logarithmic Derivative (SLD) one, showing that the AI measure alone may fail to adequately quantify this gap. Assessing the determinant of the Quantum Fisher Information Matrix (QFIM) is crucial for a precise characterization of the model's nature. Nonetheless, the AI measure still plays a relevant role since it encapsulates the non-classicality of the model in one scalar quantity rather than in a matrix form (i.e., the Uhlmann curvature).

Find the preprint on arXiv here!

We are excited to announce the new preprint by group members Alec Boyd and Felix Binder, with Prof. James P. Crutchfield (UC Davis) and Prof. Mile Gu (NTU Singapore).

Efficiently harvesting thermodynamic resources requires a precise understanding of their structure. This becomes explicit through the lens of information engines -- thermodynamic engines that use information as fuel. Maximizing the work harvested using available information is a form of physically-instantiated machine learning that drives information engines to develop complex predictive memory to store an environment's temporal correlations. We show that an information engine's complex predictive memory poses both energetic benefits and risks. While increasing memory facilitates detection of hidden patterns in an environment, it also opens the possibility of thermodynamic overfitting, where the engine dissipates additional energy in testing. To address overfitting, we introduce thermodynamic regularizers that incur a cost to engine complexity in training due to the physical constraints on the information engine. We demonstrate that regularized thermodynamic machine learning generalizes effectively. In particular, the physical constraints from which regularizers are derived improve the performance of learned predictive models. This suggests that the laws of physics jointly create the conditions for emergent complexity and predictive intelligence.

We're excited about the work just presented by Marco Radaelli and Felix Binder, together with Joey A. Smiga and Gabriel T. Landi (Univ. Rochester)!

We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling. This unraveling picture corresponds to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation in the single-shot scenario. Finally, we consider the case where some information is lost in data compression/post-selection, and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.

Have a look on arXiv here!

Fresh off the press: new publication on quantum batteries

Our group's most recent output is a new paper on work precision and fluctuations in quantum battery charging that has just been published in Physical Review E. With this work, we go beyond the usual average quantities and characterise deviations in terms of fluctuations in the process and precision of the resulting outcome of quantum battery charging. The central results are optimal and near-optimal protocol for minimising these two forms of imprecision. The paper is joint work between Pharnam Bakhshinezhad, Beniamin R. Jablonski and Nico Friis at TU Wien, and Felix Binder.

It is available for open-access download on the journal's website here!

We're very excited about the new result just published in Quantum, in collaboration with Lucas B. Vieira (IQOQI Vienna), Giuseppe Vitagliano (TU Vienna), and Costantino Budroni (University of Pisa)!

What can be learned about an uncontrollable (quantum) environment by only looking at a part of it? It turns out, quite a lot. In this work, we show that temporal correlation of a small, controllable probe system allow one to deduce pertinent properties of an uncontrollable environment it is coupled to. Specifically, we derive environment dimension witnesses based on observable joint probabilities for sequences of outcomes of a sequentially measured system. Concretely, by exploiting the inherent symmetry and sparsity of the problem we provide a numerically tractable converging hierarchy of semidefinite programs for the computation of these witnesses, thus rendering them experimentally accessible. Our approach highlights the wealth of information contained in temporal correlations and the potential of new techniques for characterizing large complex quantum systems by means of a small probe alone.

Have a look on Quantum journal here!

Together with Abhisek Panda and Sai Vinjanampathy (both IIT Bombay), Felix Binder highlights the need for careful accounting of measurement costs in quantum heat engines.

Quantum measurement engines are heat engines that make use of a quantum measurement intervention during the engine cycle. With this work we point out that care has to be taken when accounting for hidden resource costs that are implicit to ideal quantum measurement. Carefully accounting for these hidden costs, we demonstrate that (non-quantum) thermal correlations can match and in fact outperform the efficiency of a bipartite measurement engine with entanglement. This raises the question about possible thermodynamic advantages for measurement strokes in quantum heat engines more generally.

Have a look at the paper on Physical Review A here!

Have a look at the latest paper of group member Dr. Simon Milz, in collaboration with Dr. Graeme Berk (Nanyang Technological University, Singapore), Dr. Felix Pollock, and Prof. Kavan Modi (both Monash University, Melbourne)!

A great many efforts are dedicated to developing noise reduction and mitigation methods. One remarkable achievement in this direction is dynamical decoupling (DD), although its applicability remains limited because fast control is required. Using resource theoretic tools, we show that non-Markovianity is a resource for noise reduction, raising the possibility that it can be leveraged for noise reduction where traditional DD methods fail. We propose a non-Markovian optimisation technique for finding DD pulses. Using a prototypical noise model, we numerically demonstrate that our optimisation-based methods are capable of drastically improving the exploitation of temporal correlations, extending the timescales at which noise suppression is viable by at least two orders of magnitude, compared to traditional DD which does not use any knowledge of the non-Markovian environment. Importantly, the corresponding tools are built on operational grounds and can be easily implemented to reduce noise in the current generation of quantum devices.

You can find the paper here.

We would like to welcome the new student members of our group:

Yutong Luo, MSc student at Imperial College London, will be studying thermodynamic operations and their interplay with temporal resources (such as memory and dynamical resources) for the control interactions that enable system transformations.

Luke Hodgkiss, BSc student in Theoretical Physics at Trinity, will be researching the application of (quantum) reservoir computing to parameter estimation for quantum states.

Dubhaltach McSweeney, BSc student in Physics at Trinity, will be studying Petz maps for non-Markovian multistep processes.

Rohan Kadam, BSc student in Physics at Trinity, will be studying parameter estimation problems on spin chains.

We wish them all the best of luck, and we hope they will have a nice and productive time in our group!

Have a look at our latest paper, in collaboration with Dr. Joseph A. Smiga and Prof. Gabriel T. Landi (University of Rochester, US)!

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is lost if the stochastic process is compressed into a single histogram, known as the empirical distribution. As we show, the answer is non-trivial due to the correlations between outcomes. We derive practical formulas for the resulting Fisher information for various scenarios, from generic stationary processes to discrete-time Markov chains to continuous-time classical master equations. The results are illustrated with several examples.

Read on Physical Review Research here!

We're very excited about the new result just published as a preprint by group member Dr. Simon Milz with Dr. Philip Taranto, Prof. Mio Murao (both University of Tokyo), and Assoc. Prof. Marco Túlio Quintino (Sorbonne Université).

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise from/are transmitted via interactions between a system and its environment; as such, they can be either classical or quantum. From a practical standpoint, quantum processes with classical memory promise near-term applicability: they are more powerful than their memoryless counterpart, yet at the same time can be controlled over significant timeframes without being spoiled by decoherence. However, despite practical and foundational value, apart from simple two-time scenarios, the distinction between quantum and classical memory remains unexplored. We first analyse various physically-motivated candidates regarding a suitable definition for classical memory that lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically characterise the hierarchy of multi-time memory effects in quantum mechanics, many levels of which collapse in the two-time setting, making our results genuinely multi-time phenomena.

Have a look on arXiv here!

We're happy to announce that Gustav Jäger and Minfei Zou have recently completed their Master's research internship in our group! This was the last step in completing their MSc degree in Quantum Science and Technologies at Trinity College Dublin.

During her weeks with us, Minfei explored stochastic process modelling in both classical and quantum regimes, investigating their efficient approximations with tensor network techniques.

Gustav on the other hand, studied quantum thermodynamic learning via a quantum thermodynamic agent that individually couples to single qubits of a larger initial state to extract the maximal amount of work.

We would like to thank Gustav and Minfei for their time and contributions to the group and wish them the very best of luck in their future endeavours!

We would like to thank Dr. Alexandra M. Jurgens, currently at Inria Centre at the University of Bordeaux, for her visit to our research group and Trinity College Dublin from 05/06/2023 to 11/06/2023. 

She gave a talk to the group titled "Divergent Memory: Optimal Prediction of Finite State Hidden Markov Processes".

 You can find more about her work on her personal webpage here.

We're very excited about the new result just published as a preprint by group member Dr. Simon Milz with Lucas B. Vieira (IQOQI Vienna, Austria), Prof. Giuseppe Vitagliano (Vienna University of Technology, Austria), and Prof. Costantino Budroni (University of Pisa, Italy).

What can be learned about an uncontrollable (quantum) environment by only looking at a part of it? It turns out, quite a lot. In this work, we show that temporal correlation of a small, controllable probe system allow one to deduce pertinent properties of an uncontrollable environment it is coupled to. Specifically, we derive environment dimension witnesses based on observable joint probabilities for sequences of outcomes of a sequentially measured system. Concretely, by exploiting the inherent symmetry and sparsity of the problem we provide a numerically tractable converging hierarchy of semidefinite programs for the computation of these witnesses, thus rendering them experimentally accessible. Our approach highlights the wealth of information contained in temporal correlations and the potential of new techniques for characterizing large complex quantum systems by means of a small probe alone.

Have a look on arXiv here:

https://arxiv.org/abs/2305.19175

Have a look at our latest preprint, in collaboration with Dr. Joseph A. Smiga and Prof. Gabriel T. Landi (University of Rochester, US)!

We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is lost if the stochastic process is compressed into a single histogram, known as the empirical distribution. As we show, the answer is non-trivial due to the correlations between outcomes. We derive practical formulas for the resulting Fisher information for various scenarios, from generic stationary processes to discrete-time Markov chains to continuous-time classical master equations. The results are illustrated with several examples.

You can find the preprint here on arXiv!

We are delighted to announce the work recently published on the arXiv by group member Dr. Alec Boyd, together with Jinghao Lyu and James P. Crutchfield (University of California Davis).

When reformulated as a resource theory, thermodynamics can analyze system behaviors in the single-shot regime. In this, the work required to implement state transitions is bounded by α-Renyi divergences and so differs in identifying efficient operations compared to stochastic thermodynamics. Thus, a detailed understanding of the difference between stochastic thermodynamics and resource-theoretic thermodynamics is needed. To this end, we study reversibility in the single-shot regime, generalizing the two-level work reservoirs used there to multi-level work reservoirs. This achieves reversibility in any transition in the single-shot regime. Building on this, we systematically explore multi-level work reservoirs in the nondissipation regime with and without catalysts. The resource-theoretic results show that two-level work reservoirs undershoot Landauer's bound, misleadingly implying energy dissipation during computation. In contrast, we demonstrate that multi-level work reservoirs achieve Landauer's bound and produce zero entropy.

Have a look at the paper here!

Our collaboration on 'Work Extraction from Unknown Quantum Sources' with Dominik Šafránek and Dario Rosa from the Center for Theoretical Physics of Complex Systems at the Institute for Basic Science in Daejeon, Korea has just been published in Physical Review Letters!

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery.

Check out the paper here!

We are proud to announce that our paper with Prof. Gabriel T. Landi (currently University of Rochester) and Prof. Kavan Modi (Monash University) has been accepted in New Journal of Physics!

Many real-world tasks include some kind of parameter estimation, i.e., the determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic process with temporal correlations, the random variables that constitute it are identically distributed but not independent. This is the case, for instance, for quantum continuous measurements. In this article, we derive the asymptotic Fisher information rate for a stationary process with finite Markov order. We give a precise expression for this rate which is determined by the process' conditional distribution up to its Markov order. Second, we demonstrate with suitable examples that correlations may both enhance or hamper the metrological precision. Indeed, unlike for entropic information quantities, in general nothing can be said about the sub- or super-additivity of the joint Fisher information in the presence of correlations. To illustrate our results, we apply them to thermometry on an Ising spin chain, considering nearest-neighbour and next-to-nearest neighbour coupling. In this case, the asymptotic Fisher information rate is directly connected to the specific heat capacity of the spin chain. We observe that the presence of correlations strongly enhances the estimation precision in an anti-ferromagnetic chain, while in a ferromagnetic chain this is not the case.

Have a look on New Journal of Physics here!

We're very excited about the new result just published as a preprint by group member Dr. Simon Milz with Prof. Marco Túlio Quintino (Sorbonne Université, France).

Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels and channels with memory, and also higher-order operations such as superchannels, quantum combs, n-time processes, testers, and process matrices which may not respect a definite causal order. Deducing and characterising their structural
properties in terms of linear and semidefinite constraints is not only of foundational relevance, but plays an important role in enabling the numerical optimization over sets of quantum objects and allowing simpler connections between different concepts and objects. Here, we provide a general framework to deduce these properties in a direct and easy to use way. Additionally, while primarily guided by practical quantum mechanical considerations, we extend our analysis to mappings between general linear/affine spaces and derive their properties, opening the possibility for analysing sets which are not explicitly forbidden by quantum theory, but are still not much explored. Together, these results yield versatile and readily applicable tools for all tasks that require the characterization of linear transformations, in quantum mechanics and beyond. As an application of our methods, we discuss the emergence of indefinite causality in higher-order quantum transformation.

Have a look on arXiv here:

https://arxiv.org/abs/2305.01247

We're very excited about the new result just published on Quantum by group member Dr. Simon Milz with Dr. Philip Taranto (currently University of Tokio) and Dr. Thomas J. Elliott (University of Manchester).

In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics,  first and foremost because quantum measurements are invasive. Going  beyond measurement invasiveness, here we derive a novel distinction between classical and quantum processes, namely the possibility of  hidden quantum memory. While Markovian statistics of classical processes  can always be reproduced by a memoryless dynamical model, our main result shows that this is not true in quantum mechanics: We first provide an example of quantum non-Markovianity whose manifestation depends on whether or not a previous measurement is performed – an impossible phenomenon for memoryless dynamics; we then strengthen this result by demonstrating statistics that are Markovian independent of how they are probed, but are nonetheless still incompatible with memoryless quantum dynamics. Thus, we establish the existence of Markovian statistics gathered by probing a quantum process that nevertheless fundamentally require memory for their creation.

Have a look on Quantum Journal here!

Last week, the group enjoyed three days discussing physics in a friendly atmosphere and exploring the stunning grounds of Birr Castle on our first official group retreat.

The retreat was an opportunity to engage in focused scientific discussions about ongoing research projects, learn from each other, and to explore future research avenues. Not an easy thing to do sometimes in the usual busy Dublin days…

And, of course, we made time for relaxed moments exploring the incredible beauty of the Castle grounds, drinking pints, and enjoying traditional music in a local pub!

We welcome Dr. Simon Milz to our team. Simon is joining us on a Marie Skłodowska-Curie Actions (MSCA) fellowship awarded by the EU. After obtaining his PhD at Monash University in 2019 he spent three years as a Post-Doc at IQOQI Vienna before moving to Ireland. In Dublin, Simon’s work will focus on “Taming, controlling and harnessing quantum complexity” in quantum stochastic processes.

Welcome Simon!

In our most recent preprint, in collaboration with Prof. Gabriel T. Landi (Rochester University, US) we propose and explore a new algorithm to efficiently simulate quantum jump trajectories, inspired by the well-known classical Gillespie algorithm.

We also propose a Julia implementation, available on GitHub (here) and a Mathematica one (in the Melt package, here).

Have a look on arXiv here:

https://arxiv.org/abs/2303.15405

Our group has embarked on a new research collaboration titled ‘Emergence Of Objective Reality: From Qubit To Oscilloscope’ funded with US$600k by the John Templeton Foundation.

Last week we shared the project’s first results: a relation of quantum measurement to the process of thermodynamic equilibration. The open-access preprint is available via the arXiv.

The research consortium is jointly lead by Prof Felix Binder along with collaborators Dr Maximilian Lock and Dr Nicolai Friis at TU Wien in Vienna. The experimental groups of Mehul Malik (Heriot-Watt University, Edinburgh), and Jörg Schmiedmayer (TU Wien), as well as Marcus Huber’s theory group (TU Wien), and philosopher Lina Jansson (University of Nottingham) are collaborators. In Dublin, Dr. Alessandro Candeloro, who joined us as postdoctoral researcher last month, is leading the investigations.

The central aim of the research project is to tackle one of the longest-standing unsolved questions in physics: how does the everyday world we see emerge from microscopic quantum physics? The consortium will address this question by taking a thermodynamic perspective.

The ‘measurement postulate’ at the core of quantum theory is seemingly in conflict with the laws of thermodynamics which lie at the core of physics as a whole. This raises the question: why does this ‘measurement’ postulate seem to not only be verified by quantum experiments in laboratories around the world but moreover give rise to modern quantum technologies such as quantum computing? This makes it all the more important to address the problem with a thermodynamic perspective and the modern tools of quantum and non-equilibrium thermodynamics. The team will not only attempt to reconcile measurement with thermodynamics but in fact reveal measurement as a natural consequence of thermodynamic processes.

The results of this project will be of immense value to our most fundamental understanding of physics and will also bear direct impact on emerging quantum technologies and on thermodynamics at the nanoscale. The kick-off meeting was held in the Atominstitut in Vienna (group picture below). Over three days, the researchers shared initial results and constituted working groups for the coming two years. The project will culminate with a planned international conference at Trinity College Dublin in summer 2024.