Seminars

Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns out that that many measurement assemblages used in quantum information theory as well as for studying the foundations of quantum mechanics are entirely determined by symmetry; moreover, starting from a certain symmetry group, novel types of measurement sets can be constructed. The insight gained from symmetry allows us to easily determine whether the measurements in the set are incompatible under noisy conditions, i.e., whether they can be regarded as genuinely distinct ones. In addition, symmetry allows to identify finite sets of measurements having a high sensitivity to reveal the quantumness of distributed quantum states.

It is of foremost importance, both from the foundational and technological point of view, to understand what components of the quantum theory are responsible for quantum supremacy, i.e. the potential ability of quantum computers to solve problems that cannot be solved efficiently on classical machines. One of the most promising ways to achieve this is to identify sub-theories of the quantum theory that can be efficiently simulated on classical computers, and the corresponding quantum resources (gates or states) that are responsible for the quantum speed-up. In this talk I will present the resource-theoretic approach to quantum computation, explain how it could be employed to develop a unified scheme for classical simulation of universal quantum circuits and, finally, I will describe a particular algorithm that allows one to simulate Clifford+T circuits with state-of-the-art run-time scaling.

Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the N-cycle scenarios with odd N to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fractions. In this context, the results show the emergence of non-contextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of non-contextuality with that of objectivity under the Quantum Darwinism process. We also take the opportunity to present recent developments in classical limits in Generalized Probabilistic Theories.

Most of the entropy in the current universe is believed to be in the form of Bekenstein-Hawking (BH) entropy of super-massive black holes. This entropy is proportional to the area of the horizon in units of Planck area, or, alternatively, proportional to the square of the mass of the black hole in units of Planck mass. In the “strong interpretation” BH entropy is assumed to satisfy Boltzmann’s formula S = log N. The question then arises what is the huge phase space volume N available to the universe after a gravitational collapse, but not before. Inspired by recent proposals for table-top experiments to show (or disprove) that gravity acts quantum-mechanically, I will discuss the possibility that N can be a massive entanglement of the matter in black hole with its own gravitational field, and some consequences of such an idea. This is joint work Michal Eckstein and Pawel Horodecki, available as [arXiv:1912.08607].

Note from the organisers: On behalf of the director of KCIK, prof. Karol Życzkowski, we have the pleasure to invite you to the seminar “Mathematical Aspects of Quantum Theory”. The seminar will be taking place biweekly on Tuesdays at 10:10 am in the cosy KCIK building in Sopot (http://kcik.ug.edu.pl/contact.php?go=details). The goal of the seminar is to foster inspiring discussions in a friendly informal atmosphere. There will be coffee, tea and cakes waiting for you from 9:40! Should you wish to give a talk during the seminar, please contact the organisers: Michał Eckstein, michal@eckstein.pl; Ryszard Kostecki, Ryszard.Kostecki@fuw.edu.pl.

I will discuss two extensions of the standard theory of open quantum systems. The first concerns the heat current flowing through a system between two baths, quantified by its generating function. As shown previously the corresponding system functional has the form of the Feynman-Vernon influence action, but with a time shift in some of the kernels. For harmonic oscillator baths interacting with a qubit through a spin-boson coupling I will show how to compute this functional under the non-interacting blip approximation (NIBA). The generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. I will also discuss numerical examples showing rectification of the heat current. The second concerns a qubit interacting with a fermionic bath by a Frölich polaron coupling (one boson– two fermions), as an example of a non-harmonic bath. Since the path integrals are not Gaussian the Feynman-Vernon action cannot be obtained in closed form, but contains terms of all orders in the system histories. I will discuss the quadratic terns, which correspond to standard Feynman-Vernon theory, and the quartic terms, being the first correction. This is joint work with Brecht Donvil and Kirone Mallick, available as [arXiv:1911.00427], and with Jan Tuziemski [in preparation].

Quantum communication offers a selection of methods for absolutely secure exchange of information. There are two particular links which are used in practice: fibers and free space. The latter implemented using satellites is more challenging, but offers substantially longer ranges.During my talk I will present two projects running in our lab at Nicolaus Copernicus University, which are related to satellite based quantum communication. The first one aims in building a ground station for a satellite receiver link. The second one is a joint effort with Syderal Polska and Gdansk University, where the goal is to build a satellite-grade polarization entanglement controller.

The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterizes the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously known bounds for this class of channels.

Abstract of the paper: The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard’s engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory–bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.
Link to the paper: https://arxiv.org/abs/1806.00025

We study the classicality of a finite quantum system, called environment, defined by commutativity of the associate operator algebra, given sequential measurements on the environment. We demonstrate by constructing a scheme of probing from the pure-dephasing-type interaction with a qudit and preparation-evolution-measurement protocol thereon, the weak measurement sequence on the studied environment can be induced and some characteristics of the environment can be extracted from measurement statistics. From the general measurements on the environment, we consider its Kolmogorov consistency, the situation when a shorter length joint probability can be extracted from the longer one by summing the missing all possible intermediate outcomes. We provide general criteria for equivalence between Kolmogorov consistency of the statistics for arbitrary measurements and commutativity property of operator algebra of the environment, and apply the criteria to show explicitly for the induced measurements. As a result, we show that Kolmogorov consistency of the probability can be considered as a quantumness witness for its corresponding operator algebra of the environment if the conditional Hamiltonians are all non-degenerate. For the qubit, the equivalence can be obtained in general if one considers two axes of measurements namely X and Y.

As I will shortly move to ICTQT, in this talk I will try to give an overview of my work during the PhD. During this period I worked mainly on open quantum systems, applying collisional models to study both cascade systems (i.e. systems with a chiral propagation of information) and thermodynamic problems. On the other side, I also worked on potential engineering, that is, the design of potential profiles in order to obtain quantum states with specific properties or to perform specific tasks.