Mohammad Mehboudi

Postdoc @ University of Geneva

Friday July 1 – 12.30 BST

Feasible measurements for thermometry of Gaussian quantum systems 

We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This contrasts with the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while photo-detection-like measurements do it for when the temperature tends to zero. Lastly, we present an example where, despite being sub-optimal, Gaussian measurements can exploit bath induced correlations to enhance thermometry precision at extremely low temperatures. Our results therefore put forward an experimentally realizable thermometry protocol for Gaussian quantum. 
1. arXiv:2110.02098 
2. Phys. Rev. Lett. 128, 040502 (2022)

Michele Campisi 

Faculty @ NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa 

Friday July 1 – 12.00 BST

Observation of quantum enhanced information erasure

We study Information erasure is one of the basic operations that allow computers, classical and quantum alike, to work. Recent research has elucidated the microscopic mechanisms that are  the basis of the physics of information erasure and their energetic cost. Experiments have been carried either in the classical regime (e.g., using optically trapped colloidal particles), or in the quantum regime (e.g., using nanomagnets). Here we employ a quantum annealer to experimentally study the process of information erasure in a macroscopic register whose degree of quantumness can be tuned. This allowed the unprecedented possibility to observe the genuine impact that quantum phenomena have on the physics of information erasure. We report evidence of a triple quantum advantage: the quantum assisted erasure is more effective, faster and more energy efficient. We also observe that the quantum enhancement is so strong that it enables a cooperative erasure of the information individually carried by each qubit forming the register, and that happens with an energy dissipation close to the Landauer bound. We thus demonstrated an effective and energy efficient method to prepare ensembles of qubits in a state of high purity and long time duration, which is a promising tool for quantum computing applications.

Alberto Rolandi 

Postgraduate @ University of Geneva 

Friday July 1 – 11.30 BST

Finite-time Landauer principle at strong coupling 

Landauer’s principle gives a fundamental limit to the thermodynamic cost of erasing information. Its saturation requires a reversible isothermal process, and hence infinite time. We develop a finite-time version of Landauer’s principle for a quantum dot strongly coupled to a fermionic bath. By solving the exact non-equilibrium dynamics, we optimize erasure processes (taking both the dot’s energy and system-bath coupling as control parameters) in the slow driving regime through a geometric approach to thermodynamics. We find analytic expressions for the thermodynamic metric and geodesic equations, which can be solved numerically. Their solution yields optimal finite-time processes that allows us to characterise a fundamental finite-time correction to Landauer’s bound, fully taking into account non-markovian and strong coupling effects. 

Alvaro Alhambra

Faculty @ Max Planck Institute for Quantum Optics, Germany

Friday July 1 – 10.45 BST

Quantum many-body systems in thermal equilibrium: correlations and classical simulation

There are numerous models of interacting many-body quantum systems whose physics we would like to probe and better understand. This notably includes situations in which the systems at hand are at thermal equilibrium with its environment. 

Due to the inherent complexity of quantum mechanics, one might expect that those equilibrium states will typically be very complex, and hard to describe via direct means or classical algorithms. At the same time, the effect of thermal fluctuations, together with our intuition from thermodynamics, point in the opposite direction: a system at equilibrium should have a simple description. 

In this talk, we aim to clarify the product of this tension. To do so, we explain how and when quantum systems in thermal equilibrium can be shown to have simpler features and descriptions than general quantum states. This includes mathematical results on the nature of the internal correlations of these systems, such as area laws, as well as provably efficient classical algorithms for their description, mostly involving tensor networks. 

Saulo V. Moreira 

Postdoc @ Lund University 

Friday July 1 – 9.45 BST

Extractable work in a Szilard engine with a finite-size reservoir

The Szilard engine is a paradigmatic protocol in thermodynamics when it comes to the question of how much work can be extracted from a system coupled to a single thermal reservoir, by means of performing measurement and feedback. Originally conceived as a thought experiment by Szilard [1], experimental realizations of the engine have been implemented over the last few years, for example in the context of nanodevices such as quantum dots [2,3]. In an ideal Szilard engine, in which the system is coupled to an infinite-size bath at constant temperature, the extractable work has an upper bound, reaching k_BT ln 2 for a quasi-static, large amplitude cycle. 
Here, we aim to study how the extraction of work in a Szilard engine is impacted by finite-size reservoirs. We focus on a system constituted of a quantum dot, which is, in turn, coupled to a finite-size fermionic reservoir. Due to the exchange of heat between the quantum dot and the reservoir, the temperature of the reservoir develops fluctuations in time. We find that the maximum amount of work that can be extracted is always lower than in the ideal Szilard engine, with infinite size reservoirs. Moreover, in the limit of large but finite-size reservoirs, the difference in extractable work is inversely proportional to the heat capacity of the reservoir. 
Moreover, we compare our results with previously derived upper bounds for the extractable work derived for finite-size reservoirs [4,5], and show that our results are consistent with these bounds. 

[1] L. Szilard. Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen, Z. Physik 53, 840–856 (1929). 
[2] J. V. Koski, V. F. Maisi, J. P. Pekola and D. V. Averin. Experimental realization of a Szilard engine with a single electron, Proc Natl Acad Sci 11, 13786 (2014). 
[3] D. Barker, M. Scandi, S. Lehmann, C. Thelander, K. A. Dick, M. Perarnau-Llobet, and V. F. Maisi. Experimental Verification of the Work Fluctuation-Dissipation Relation for Information-to-Work Conversion, Phys. Rev. Lett. 128, 040602 (2022). 
[4] R. Clausius. Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie, Ann. Phys. 201, 353 (1865). 
[5] P. Strasberg and A. Winter. First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy. PRX Quantum 2, 030202  (2021). 

Shachar Fraenkel

Postgraduate @ Tel Aviv University

Friday July 1 – 9.15 BST

Extensive long-range entanglement in a nonequilibrium steady state 

Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of noninteracting fermions at zero temperature in the presence of a scatterer. In our previous work [1] we found an unusual scaling law for the entanglement entropy of a subsystem that is far away from the scatterer. Our exact results showed that the entanglement entropy of such a subsystem obeys an extensive (volume-law) scaling along with an additive logarithmic correction. 
In this new work, we show that disjoint intervals located on opposite sides of the scatterer and within similar distances from it display volume-law entanglement regardless of their separation, as measured by their fermionic negativity [2] and coherent information [3]. We employ several complementary analytical methods to derive exact expressions for the extensive terms of these quantities and, given a large separation, also for the subleading logarithmic terms. Remarkably, our results imply in particular that far-apart intervals which are positioned symmetrically relative to the scatterer are more strongly entangled than if we had reduced the distance between them by choosing one of these intervals to be closer to the scatterer. 
The strong long-range entanglement is generated by the coherence between the transmitted and reflected parts of propagating particles within the bias-voltage window, despite the fact that only single particles are scattered independently. The generality and simplicity of the model suggest that this behavior should characterize a large class of nonequilibrium steady states. 

[1] S. Fraenkel and M. Goldstein, Entanglement measures in a nonequilibrium steady state: Exact results in one dimension, SciPost Phys. 11, 85 (2021). 
[2] H. Shapourian, K. Shiozaki, and S. Ryu, Partial time-reversal transformation and entanglement negativity in fermionic systems, Phys. Rev. B 95, 165101 (2017). 
[3] M. Horodecki, J. Oppenheim, and A. Winter, Partial quantum information, Nature 436, 673 (2005). 

Ju-Yeon Gyhm

Postgraduate @ Seoul National University (SNU)

Friday July 1 – 8.45 BST

Quantum Charging Advantage Cannot Be Extensive Without Global Operations 

Quantum batteries are thermal devices, which store energy at quantum states and convert it to usable energy. They have numerous possibilities to be applied significant technology, due to their speed of charging and releasing energy which has at most quadratic scaling with cells over the classically achievable linear scaling. The paper, “Quantum Charging Advantage Cannot Be Extensive Without Global Operations” (going to be published at Physical Review Letters as Editors’ Suggestion) shows the general bound of charging speed and the necessary condition to reach the quadratic scaling derived from the bound. 
Quantum batteries’ state storing energy at the battery Hamiltonian $\hat{H}$ is evolved by the driving Hamiltonian $\hat{V}$. This is the basic protocol of Quantum batteries and gives a crucial bound for us. We show that the maximum energy change $\Delta E$ by the first time perturbation term $\hat{V}t$ decide the bound of the power. It is simply written as equation $|P|\leq \Delta E \|\hat{V}\|$ which gives the condition to obtain quadratic scaling. 
To achieve quadratic scaling, a global charging protocol, which charges all the cells collectively, needs to be employed. Meanwhile, It is not a sufficient condition. We found a case that the batteries evolved by the global operator have the power increasing with linearly with cells. 
We showed the significant condition for quantum batteries. This concludes the quest on the limits of charging power of quantum batteries and adds to other results in which quantum methods are known to provide at most quadratic scaling over their classical counterparts. 
cf. I changed my academic name as Ju-Yeon Gyhm from Juyeon Kim. The First author of the paper referred to in the abstract is me. 
Kim, J., Rosa, D., & Šafránek, D. (2021). Quantum Charging Advantage Cannot Be Extensive Without Global Operations. arXiv preprint arXiv:2108.02491. 

Armen Allahverdyan

Faculty @ Yerevan Physics Institute, Armenia

Friday July 1 – 8.00 BST

Dissipative search of an unstructured database

The search of an unstructured database amounts to finding one element having a certain property out of $N$ elements. The classical search with an oracle checking one element at a time requires on average $N/2$ steps. The Grover algorithm for the quantum search, and its unitary Hamiltonian evolution analogue, accomplish the search asymptotically optimally in $O(\sqrt{N})$ time steps. Here we propose a new computational model based on dissipative dynamics, where the quantum search is reformulated as a problem in non-equilibrium statistical mechanics. Now the search amounts to relaxing to the ground state for a quantum system having a specific, gapped energy spectrum. We show that under proper conditions, a dissipative Markov process in the $N$-level system coupled to a thermal bath leads to the system’s relaxation to the ground state during time $O(\ln N)$. 

[A. E.  Allahverdyan and D. Petrosyan, Dissipative search of an unstructured database, Phys. Rev. A 105, 032447 (2022)].