Titles and Abstracts
Eugene Polzik, University of Copenhagen
Measurement of Motion Beyond the Heisenberg Uncertainty Bound
Gorjan Alagic, QMATH, University of Copenhagen
Internet cryptography for quantum states
Quantum mechanics has profound implications for cryptography. It tells us that perfectly secure key exchange is possible, and that factoring is not a good basis for encryption. More generally, it tells us that quantum data and quantum computation are more fundamental than their classical counterparts. One consequence is that the Internet of the future will likely be “fully-quantum,” with all participants able to prepare, send, and compute on quantum states.
In this talk, we will discuss how such an Internet might be secured. One starting point is to place encryption of quantum data on the same foundations as modern Internet encryption. Then, we might attempt to translate many of the great achievements of classical cryptography to the quantum setting. In some cases (such as CPA-secure encryption), this is a straightforward matter of combining the right classical and quantum primitives. In general, new ideas are required to achieve more advanced things like unforgeability, CCA-security, and fully-homomorphic encryption. Finally, I will mention some primitives (such as black-box obfuscation) that are impossible classically but may exist in some form in the fully-quantum setting.
Torben Krüger, IST Austria
Local eigenvalue statistics for random matrices with general short range correlations
The statistics of eigenvalues of random matrix ensembles often exhibits universal behavior as the sizes of the matrices grow to infinity. By this we mean that statistical quantities (e.g. k-point correlation functions of eigenvalues, fluctuations of eigenvalues around their expected positions, distributions of gap sizes between neighboring eigenvalues, etc.) do not depend on most of the details of the model. We prove such a universality statement for non-centered random matrices H with general short range correlations. Our analysis shows that the resolvent G(z) = 1/(H-z) of of the random matrix H approaches a deterministic limit M(z) as long as the spectral smoothing Im[z] is larger than the typical eigenvalue spacing. The limit satisfies the Matrix Dyson equation - 1/M = z - E[H] + E[(H-E[H])M(H-E[H])] which only depends on the second moments of the entries of H. The key novelty is a detailed stability analysis of this non-linear matrix valued equation in asymptotically infinite dimensions.
Renato Renner, ETH Zürich
An Information-Theoretic View on the Copenhagen Interpretation
Information theory, apart from its many technological implications, also gives a novel perspective on the foundations of quantum mechanics. To illustrate this, I will present a theorem which provides information-theoretic constraints on how the formalism of quantum theory can be interpreted. The theorem implies that interpretations in the spirit of Copenhagen are generally inconsistent in scenarios involving multiple agents. This shows that the use of a suitable interpretation of
quantum theory is also relevant to cryptography, where such multi-agent
scenarios are ubiquitous.
Reinhard Werner, University of Hannover (Outreach Lecture)
The simple argument that changed the world view of physics
Quantum Theory has the reputation of being unintuitive and perhaps impossible to understand. Indeed it deviates from the classical world view in an essential way. But is this really necessary? I will tell a simple story illustrating the argument (originally due to Bell) that under minimal assumptions, and on minimal empirical input, some key features of quantum mechanics are inevitable. This includes a simple version of Bohr's complementarity, the no-cloning theorem, and other elements that allow us to think reliably about quantum systems and to develop appropriate intuitions.
Harry Buhrman, QuSoft Amsterdam
Quantum Computing and Complexity Theory
Quantum computers hold great promise as the next generation hardware. They are based on counter-intuitive phenomena from quantum mechanics, like superposition, interference, and entanglement. The basic building block of a quantum computer is a quantum bit or qubit, which unlike a classical bit can be in a quantum superposition (a simultaneous combination) of both 0 and 1. In the 1990s it was demonstrated that, for specific problems, quantum algorithms run on a quantum computer can massively outperform classical computers. The famous quantum algorithm of Peter Shor shows that a quantum computer can factor large numbers and thus breaks most of modern-day cryptography.
Quantum computers appear to have an advantage over the classical computation paradigm. However, it i unclear how large this advantage is. What is the power of a quantum computer and how does it relate to the classical computation paradigm? In this talk I will highlight some of the recent results and ideas relating classical and quantum information processing.
Shelby Kimmel, University of Maryland
What is the connection between the effective resistance of electrical circuits and quantum algorithms?
I will answer the question in the title. I will also describe a new quantum algorithm for Boolean formula evaluation and an improved analysis of an existing quantum algorithm for st-connectivity. Joint work with Stacey Jeffery.
Krzysztof Gawedzki, ENS de Lyon
A field-theoretic construction of topological invariants for crystals with time-reversal symmetry
I shall discuss a specific construction of Z_2-valued invariants of topological phases for 2d and 3d time-reversal symmetric crystals, both static and periodically driven.
Charles Marcus, QDev, University of Copenhagen
Scaling relations in the Superconductor- insulator transition
Charles Bennett, IBM Watson
Scientific Multiculturalism in Quantum Informatics
Physicists, mathematicians and engineers, guided by what has worked well in their respective disciplines, acquire different scientific tastes, different notions of what constitutes an interesting, well-posed problem or an adequate solution. While this has led to some frustrating misunderstandings, it has invigorated the theory of communication and computation, enabling it to outgrow its brash beginnings with Turing, Shannon and von Neumann, and develop its own mature scientific taste.
Klaus Mølmer, University of Aarhus
The Ichtyosaur in the room
Jeroen Zuiddam, CWI Amsterdam
Creating networks of entangled pairs: tensor surgery and the laser method
Given two multipartite quantum states, can we transform one into the other with nonzero probability by performing only local operations and classical communication (SLOCC)? This question turns out to be hard! (Complexity theorists say: "NP-hard".) We study a specific instance of this question, namely: how many Greenberger-Horne-Zeilinger (GHZ) states are required to construct a network of Einstein-Podolsky-Rosen (EPR) pairs by SLOCC? Any graph defines such a network by associating an EPR pair to each edge of the graph. In the language of tensors, our question amounts to studying the tensor rank of these networks. With "tensor surgery", we obtain asymptotically optimal constructions for all cycle graphs. With the "laser method", we obtain constructions for complete graphs that outperform the constructions implied by the fastest matrix multiplication algorithms.
Jérémy Sok, QMATH, University of Copenhagen
Dirac operators with magnetic links
We introduce Dirac operators on the three-sphere with singular magnetic fields. These magnetic fields are supported on links, a collection of disconnected smooth closed curves. Each curve is a field line carrying a flux which exhibits a 2-periodicity. By tuning a flux from 0 to 2, we obtain a family of Dirac operators whose spectral flow (that is the net number of eigenvalues crossing positively 0) depends on the linking numbers of the different curves and their writhes.
Roberto Ferrara, QMATH, University of Copenhagen
Private states, quantum data hiding and the swapping of perfect secrecy
I will briefly recall the basic elements of the BB84 and E91 quantum key distribution schemes so that I can motivate the introduction of private states. These states are noisy versions of EPR pairs but give the same amount of key nonetheless. However, as opposed to EPR pairs, there exist private states that are useless for quantum communication tasks like teleportation. I will explain how this is due to quantum data hiding, the
effect of hiding classical data from local measurements into bipartite states,
and state it formally in a theorem. Finally, I will briefly mention how this affects our understanding of quantum key distribution across a quantum repeater station.
Based on arXiv: 1609.04696.
Robert Seiringer, IST Austria
Stability of many-body systems with point interactions
We present a proof that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m∗. The value of m∗ is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also present a rigorous version of the Tan relations valid for all wave functions in the domain of the Hamiltonian of this model.
Ivan Damgaard, University of Aarhus
The Orthogonal Vector Problem and Applications to Leakage Resilient Cryptography
In the orthogonal vector problem, two parties Alice and Bob want to interactively create vector u for Alice and v for Bob such that u,v are random, subject to u and v being orthogonal. We want that the protocol emulates (almost perfectly) an ideal case where u and v are supplied by an oracle, in the following sense: an adversary who gets partial information from Alice's and Bob's memories learns nothing about u and v, that he could not also learn in the ideal case. We show that the problem cannot be solved using classical communication, but can be solved by a simple "prepare and measure" type quantum protocol. We also present some applications of the solution to leakage resilient cryptography.
Joint work with Jesper Buus Nielsen and Fred Dupuis.