Seminars

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.

Link to the paper: https://arxiv.org/abs/1903.05025

The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown, however, that all entangled states lead to nonclassical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand, we demonstrate that every state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlations. On the other hand, we show the strength of a particular entangled state and entangled measurement for teleportation—as quantified by the robustness of teleportation—precisely characterizes their ability to offer an advantage in the task of subchannel discrimination with side information. This connection allows us to prove that every entangled state outperforms all separable states when acting as a quantum memory in this discrimination task. Finally, within the context of a resource theory of teleportation, we show that the two operational tasks considered provide complete sets of monotones for two partial orders based on the notion of teleportation simulation, one classical and one quantum.
Link to the paper: https://arxiv.org/abs/1908.05107

Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr and later realised more technically by Kochen and Specker. Isham and Butterfield put contextuality at the heart of their topos-based formalism and gave a reformulation of the Kochen-Specker theorem in the language of presheaves. Here, we broaden this perspective considerably (partly drawing on existing, but scattered results) and show that apart from the Kochen-Specker theorem, also Wigner’s theorem, Gleason’s theorem and Bell’s theorem relate fundamentally to contextuality. We provide reformulations of the theorems using the language of presheaves over contexts and give general versions valid for von Neumann algebras. This shows that a very substantial part of the structure of quantum theory is encoded by contextuality.
Link to the paper: https://arxiv.org/abs/1910.09591

Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context. First, we find that quantum entanglement shared between senders can substantially boost the capacity of a classical MAC. Second, we find that optimal performance of a MAC with bounded-size inputs may require unbounded amounts of entanglement. Third, determining whether a perfect communication rate is achievable using finite-dimensional entanglement is undecidable. Finally, we show that evaluating the capacity region of a two-sender classical MAC is in fact NP-hard.
Link to the paper: https://arxiv.org/abs/1909.02479

The study of polynomials that are positive on certain sets has a rich history, going back to Hilbert’s seventeenth problem. Here we will look at multivariate polynomials (and more generally, contractions) that have matrices as their variables. These are constructed such that they yield positive semi-definite expressions whenever they are evaluated on the positive cone, extending the well-known concept of positive maps as used in entanglement theory to the multilinear case. We will present connections to polynomial identity rings and central polynomials, concepts that found applications in quantum information in the context of MPS bond dimension witnesses and remote time manipulation.
Link to the paper: https://arxiv.org/abs/2002.12887

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).

Two identical photons impinging on different arms of a balanced beam splitter always end up grouped together. In other words, the probability that they stay separate vanishes. Finding such forbidden outcomes is, in general, a demanding task when the number of particles and modes increases. The paper [Phys. Rev. Lett. 120, 240404 (2018)] shows a link between the suppressed events and the symmetries of the input state and the multiport. I will present this result and some of its consequences.

Link to the paper: https://arxiv.org/abs/1801.07014

The 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.

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.