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We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice…
This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations…
Understanding the mechanism of high-temperature superconductivity is among the most important problems in physics, for which quantum simulation can provide new insights. However, it remains challenging to characterize superconductivity in…
When measuring quantum spins at two or more different times, the later measurements are affected by measurement backaction occurring due to the earlier measurements. This makes the measurement of temporal quantum correlation functions…
We describe a new and experimentally feasible protocol for performing fundamental tests of quantum mechanics with massive objects. In our approach a single two level system is used to probe the motion of a nanomechanical resonator via…
The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla--system couplings, that is applicable to arbitrary…
A limitation of analog quantum simulators based on cold atoms in optical lattices is that readout is typically limited to observables diagonal in the charge basis, i.e., densities and density correlation functions. To overcome this…
Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution,…
The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both, fundamental and technological importance. Here, we address such question by combining tools from quantum…
We measure the temporal pair correlation function $g^{(2)}(\tau)$ of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed {\it in situ} using a local, time-resolved…
We propose a protocol for the scalable quantum simulation of SU($N$)$\times$U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices in both one- and two-dimensional systems. The protocol exploits the combination of…
Analog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the…
We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many…
We propose a minimal model to study the real-time dynamics of a $\mathbb{Z}_2$ lattice gauge theory coupled to fermionic matter in a cold atom quantum simulator setup. We show that dynamical correlators of the gauge fields can be measured…
After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity where it can be used to investigate complex quantum processes. Planning of new experiments and upgrading…
The properties of strongly-coupled lattice gauge theories at finite density as well as in real time have largely eluded first-principles studies on the lattice. This is due to the failure of importance sampling for systems with a complex…
We review a recently developed theoretical approach to the experimental detection and quantification of bipartite quantum correlations between a qubit and a d dimensional system. Specifically, introducing a properly designed measure Q, the…
The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$\frac{1}{2}$ system simultaneously…
Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…