Other

At the heart of the quantum measurement problem lies the ambiguity about exactly when to use the unitary evolution of the quantum state and when to use the state-update in dynamics of quantum mechanical systems. In the Wigner’s friend gedankenexperiment, different observers (one of whom is observed by the other) describe one and the same interaction differently. One – the friend – uses the state-update rule and the other – Wigner – chooses unitary evolution. This can lead to paradoxical situations in which Wigner and his friend assign different probabilities to the outcomes of subsequent measurements. In my talk, I will apply the Page-Wootters mechanism (PWM) as a timeless description of the Wigner's friend-like scenario. This description assigns one timeless state to the entire experimental scenario from which it is possible to derive probabilities without the need to involve the evolution of the quantum state during – and in-between – measurements. I will consider several rules for assigning two-time conditional probabilities within the PWM. All of these reduce to standard (“textbook”) rules for non-Wigner’s friend scenarios. However, when applied to the Wigner’s friend setup, they differ. Each rule potentially resolves the probability-assignment paradox in a different way. Moreover, one rule imposes that a joint probability distribution for the measurement outcomes of Wigner and his friend is well-defined only when Wigner’s measurement does not disturb the friend’s memory, in agreement with the recent “no-go theorem for observer-independent facts

(with Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, and Esteban Castro-Ruiz)

This talk is a progress report on ongoing research. I will explain what resource theories have to do with real algebraic geometry, and then present a preliminary result in real algebraic geometry which can be interpreted as a theorem on asymptotic and catalytic resource orderings.

It reproves the known criterion for asymptotic and catalytic majorization in terms of Rényi entropies, and generalizes it to any resource theory which satisfies a mild boundedness hypothesis. I will sketch the case of matrix majorization as an example.

Cosmological simulations of galaxy formation have evolved significantly over the last years.
In my talk I will describe recent efforts to model the large-scale distribution
of galaxies with cosmological hydrodynamics simulations. I will focus on the
Illustris simulation, and our new simulation campaign, the IllustrisTNG
project. After demonstrating the success of these simulations in terms of
reproducing an enormous amount of observational data, I will also talk about
their limitations and directions for further improvements over the next couple
of years.

We show that a generic many-body Hamiltonian can be uniquely reconstructed from a single pair of initial-final states under the unitary time evolution. Interesting it is, this method is not practical due to its high complexity. We then propose a practical method for Hamiltonian reconstruction from multiple pairs of initial-final states. The stability of this method is mathematically proved and numerically verified.

This work is joint with Liujun Zou and Timothy Hsieh.

VisIt (https://wci.llnl.gov/simulation/computer-codes/visit/) is an interactive, powerful visualization, animation, and analysis tool.

VisIt is an open source and available for Unix, Windows or Mac users.

In this tutorial, after a brief introduction of VisIt, we will walk through several basic plotting/animation functions by using some toy data.

Results from the first digital quantum simulation of an SU(2) gauge theory are presented. This was done by analytically constructing gauge-invariant states and implementing a Trotterized time evolution operator for that basis on superconducting hardware. By using error mitigation techniques, electric energy measurements could be reliably extracted following one Trotter-Suzuki time step. This work is a small but important step toward determining what field-theoretic calculations will be possible using near-term devices.

In quantum spin systems, the existence of a spectral gap above the ground state has strong implications for the low-energy physics. We survey recent results establishing spectral gaps in various frustration-free spin systems by verifying finite-size criteria. The talk is based on collaborations with Abdul-Rahman, Lucia, Mozgunov, Nachtergaele, Sandvik, Yang, Young, and Wang.

Analytic renormalisation "à la Speer" using a multivariable approach typically leads to meromorphic germs in several variables whose poles are linear.  In particular,  Feynman integrals, multizeta functions and their generalisations, namely  discrete sums on cones and discrete sums associated with trees give rise to meromorphic germs at zero with linear poles. We shall present  a multivariable renormalisation scheme which amounts to a minimal subtraction scheme in several variables. It preserves locality in so far as the  evaluation at poles is expected to factor  on functions with independent sets of variables. Inspired by Speer, we shall discuss a class of generalised evaluators that do the job. Using a theory of  Laurent expansions  on meromorphic germs with linear poles at zero, we shall relate these generalised evaluators to the geometry of cones.

This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang.