**History of Mathematical Aspects of Quantum Theory Seminar**

**(KCIK, Sopot)**

Friday, April 24, 2020, 14:00

**Jan Tuziemski** (Stockholm University)

*Out-of-time-ordered correlation functions in open systems*

*Abstract:*

*Recent theoretical and experimental studies have shown significance of quantum information scrambling for problems encountered in high-energy physics, quantum information, and condensed matter. Due to complexity of quantum many-body systems it is plausible that new developments in this field will be achieved by experimental explorations. Therefore, a better theoretical understanding of quantum information scrambling in systems affected by noise is needed. To address this problem I will discuss indicators of quantum scrambling - out-of-time-ordered correlation functions (OTOCs) in open quantum systems. As most experimental protocols for measuring OTOCs are based on backward time evolution, two possible scenarios of joint system-environment dynamics reversal will be considered. Derivation of general formulas for OTOCs in those cases as well as a study of the spin chain model coupled to the environment of harmonic oscillators will be presented.*

Based on Phys. Rev. A 100, 062106 (2019), arXiv:1903.05025.

Friday, April 3, 2020, at 12:15

**Katarzyna Roszak** (Wrocław University of Science and Technology)

*How to detect qubit-environment entanglement in pure dephasing evolutions*

*Abstract:*

*The problem of detecting entanglement between a qubit and its environment is known to be complicated [1]. To simplify the issue, we study the class of Hamiltonians that describe the interacting system in such a way that the resulting evolution of the qubit alone is of pure dephasing type. Although this leads to some loss of generality, the pure dephasing Hamiltonian describes the dominant*

*decohering mechanism for many types of qubits. When both the qubit and the environment are initially in a pure state, their interaction leading to qubit dephasing always leads to the creation of entanglement between the two [2]. It is often assumed that such a dephasing mechanism must induce entanglement between the qubit and environment also when the environment is initially in a mixed state. We have shown that while the creation of qubit-environment entanglement in the pure dephasing case is possible when the environment is initially in a mixed state, its occurrence is by no means guaranteed [3]. We have also shown that the evolution of the environment conditional on the qubit state is qualitatively different in entangling and non-entangling scenarios [3]. This serves as a basis for possible detection of qubit-environment entanglement via measurements on only one of these subsystems. Obviously, such entanglement could be straightforwardly determined by measurements on the environment, but such measurements are rarely accessible.*

*Here, we propose a scheme for the detection of qubit-environment entanglement which requires operations and measurements on the qubit subsystem alone [4]. It relies on the fact that only for entangling evolutions does the environment behave differently in the presence of different qubit states. Hence, only if an evolution is entangling can there be a difference in the evolution of qubit coherence when the environment was allowed to relax in the presence of either qubit pointer states prior to the excitation of a superposition state. The scheme is in fact an entanglement witness. If a difference in the decay of coherence of this superposition is detected then the interaction with the environment is entangling. If not, then either there is no entanglement or the conditional evolution operators of the environment commute. We illustrate the concept with a calculation performed for a nitrogen-vacancy center in diamond, a spin qubit coupled to a nuclear spin environment that is widely used for noise spectroscopy [5].*

*References [1] B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, Phys. Rev. A 61, 062302 (2000). [2] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). [3] K. Roszak and L. Cywiński, Phys. Rev. A 92, 032310 (2015). [4] K. Roszak, D. Kwiatkowski and Ł. Cywiński, Phys. Rev. A 100, 022318 (2019). [5] L. Degen, F. Reinhard, and P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017).*

Friday, March 27, 2020, at 12:00

**Steven Bass** (Kitzbühel & UJ)

*The Cosmological Constant Puzzle - Symmetries of Quantum Fluctuations*

*Abstract: *T*he cosmological constant in Einstein's equations of General Relativity is a prime candidate to describe the dark energy that drives the accelerating expansion of the Universe and which contributes 69% of its energy budget. The cosmological constant measures the energy density of the vacuum perceived by gravitation. Experimentally, it is characterised by a tiny energy scale 0.002 eV. How should we understand this ? The quantum vacuum is described by particle physics where the mass scales that enter are very much larger. If one naively sums the zero-point energies of quantum fluctuations up to the energies where we do collider experiments at CERN then the cosmological constant comes out 10^60 times too large. Here we argue that the tiny value of the cosmological constant may be telling us something deep about the origin of symmetry in the subatomic world. The gauge symmetries which describe particle interactions may be emergent. The presentation will be given at Colloquium level and suitable for good Masters students. *

Tuesday, March 3, 2020, at 10:15

**Erik Aurell**, KTH Royal Institute of Technology (Stockholm), Jagiellonian University (Kraków)

*Quantum black holes as solvent*

*Abstract: **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]. *