Seminars

In this talk I will review the concept of “quantum batteries”: quantum systems where energy is stored and from which work can be extracted. I will focus on many-body batteries, systems composed by N identical quantum cells. In this context, I will discuss the relation between extractable work, charging power and entanglement.

We analyze the relationship between qubit-environment entanglement that can be created during the pure dephasing of the qubit and the effectiveness of the spin echo protocol. We focus here on mixed states of the environment. We show that while the echo protocol can obviously counteract classical environmental noise, it can also undo dephasing associated with qubit-environment entanglement, and there is no obvious difference in its efficiency in these two cases. Additionally, we show that qubit-environment entanglement can be generated at the end of the echo protocol even when it is absent at the time of application of the local operation on the qubit (the π pulse). We prove that this can occur only at isolated points in time, after fine-tuning of the echo protocol duration. Finally, we discuss the conditions under which the observation of specific features of the echo signal can serve as a witness of the entangling nature of the joint qubit-environment evolution.

In this presentation, we will make a wide introduction to topological quantum computing. Quantum computers use qubits in order to function and topological quantum computers use anyons, 2D particles, to encode qubits. Anyons can be determined based on the magnetic flux and the charge they are consisted of. In the first part, we will discuss the basics of group theory in order to construct an anyon model. For our anyon model, we used the group D4 and calculated the different combinations of fluxes and charges for every anyon of this model. In the second part, we will talk about the differences between anyons and 3D particles and that we (in principle) could construct a quantum computer based on the properties of anyons. Quantum gates are very sensitive to decoherence, but gates based on the rotation of anyons can guarantee a much better protection of the information. Using the Aharonov-Bohm effect, we will examine how the quantum states acquire a phase which can be used for the coding of the information. On our study, we further examined the operations which can occur between anyons and how they can be simulated with F and R matrices. In the end, we will study the simplest of all anyon models, the Fibonacci anyon model, which allows (in principle) universal quantum computing. To conduct this study, we constructed the F and R matrices for the Fibonacci anyons using some conditions known as pentagon and hexagon equations.

We discuss compatibility between various quantum aspects of bosonic fields, relevant for quantum optics and quantum thermodynamics, and the mesoscopic formalism of reduced state of the field (RSF). In particular, we derive exact conditions under which Gaussian and Bogoliubov-type evolutions can be cast into the RSF framework. To strengthen the link between the RSF formalism and the notion of classicality for bosonic quantum fields, we prove that RSF contains no information about entanglement in two-mode Gaussian states. For the same purpose, we show that the entropic characterisation of RSF by means of the von Neumann entropy is qualitatively the same as its description based on the Wehrl entropy. Our findings help bridge the conceptual gap between quantum and classical mechanics.

From the core of the matter to the stellar objects, the underlying physics relies significantly on how we understand atomic nuclei. On the other hand, the ever-puzzling nuclear interaction can be studied at various energy scales ranging from thermal neutrons to relativistic heavy-ion collisions and various sizes up to those of stars. I will introduce the correlations between finite nuclei and infinite matter, based on the liquid drop model. With the help of quantum field theory (QHD), I will elucidate modelling the nuclear interaction to describe infinite matter and neutron stars. We will discuss how the corroboration of terrestrial nuclear physics experiments, observation of neutron stars with our model could reveal properties of high-dense matter in general. I will highlight the importance of studying some exotic nuclei like the hypernuclei and proton emitters, in this regard.

In my presentation about my PhD work I will talk about Single Ion Magnets and their possible applications as the new contrast agents used in MRI. In order to obtain the magnetic properties of the selected Single Ion Magnets I have used ab-initio methods which are going to be described briefly during my talk. I will also show the accuracy of the theoretical results in comparison with the experimental data (absorption spectra and magnetic molar susceptibility).

This talk is a brief summary of my Habilitation thesis, tailored at the members of the Rada Dyscypliny, and hopefully interesting for other quantum scientists as well. I will walk you through 12 of my main publications from the last six years, touching on almost-quantum correlations, causal structures, quantum and post-quantum steering, and a resource theory of Bell-nonclassicality.

In this presentation I will focus on some numerical approaches to certain types of linear Klein Gordon equations. More particularly, I will present the numerical approach based on the Duhamel formula, where we obtain second order approximation. Modulated Fourier expansion based method will be presented as the one useful in case of highly oscillatory forcing term. Finally, I will present some splitting methods of fourth order. I will present plenty of numerical examples and comparisons.

References:
[1] Bader P., Blanes S., Casas F., Kopylov N., Novel symplectic integrators for the Klein–Gordon equation with space- and time-dependent mass, Journal of Computational and Applied Mathematics, Volume 350, 2019, 130-138 (2019).
[2] M. Condon, K. Kropielnicka, K. Lademann, R. Perczyński, Asymptotic numerical solver for the linear Klein–Gordon equation with space- and time-dependent mass, Applied Mathematics Letters,115,106935, (2021)
[3] Bauke H., Ruf M, Keitel Ch., A real space split operator method for the Klein-Gordon equation, J. Comput. Phys., 228, 24, 9092–9106, (2009).
[4] Mostafazadeh A., Quantum mechanics of Klein–Gordon-type fields and quantum cosmology, Ann. Physics 309, no. 1, 1–48 (2004).
[5] Mostafazadeh A.,Hilbert space structures on the solution space of Klein-Gordon-type evolution equations, Classical Quantum Gravity 20, no. 1, 155–171 (2003).
[6] Znojil M., Klein-Gordon equation with the time- and space-dependent mass: Unitary evolution picture, arXiv:1702.08493v1
[7] Znojil M., Non-Hermitian interaction representation and its use in relativistic quantum mechanics, Ann. Physics 385, 162–179 (2017).

“The unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement” (Bohr). The measurement process is composed of pre-measurement (quantum correlation of the system with the pointer variable), and an irreversible decoherence via interaction with an environment. The system ends up in a probabilistic mixture of the eigenstates of the measured observable. For pre-measurement stage, any attempt to introduce an `outcome’ leads, as we show, to a logical contradiction, $1=i$. This nullifies claims that a modified concept of Wigner’s Friend, who just pre-measures, can lead to valid results concerning quantum theory.

Quantum key distribution (QKD) is a method that distributes a secret key to a sender and receiver by the transmission of quantum particles (e.g. photons). Device-independent quantum key distribution (DIQKD) is a version of QKD with a stronger notion of security, in that the sender and receiver base their protocol only on the statistics of input and outputs of their devices as inspired by Bell’s theorem. We study the rate at which DIQKD can be carried out for a given bipartite quantum state distributed between the sender and receiver or a quantum channel connecting them.We provide upper bounds on the achievable rate going beyond upper bounds possible for QKD. In particular, we construct states and channels where the QKD rate is significant while the DIQKD rateis negligible. This gap is illustrated for a practical case arising when using standard post-processing techniques for entangled two-qubit state.
Based on: https://arxiv.org/abs/2005.13511