In the Theory Division, we study a wide range of topics which arise in the context of highly controlled and complex interacting quantum mechanical systems. This encompasses three main areas:

• Quantum Information Theory researches how information processing and computation are changed when using the laws of quantum mechanics, such as in quantum computers.
• Quantum Optics explores quantum phenomena as well as ways of building the basic components of quantum information processors with light, atoms, and solid state systems.
• Quantum Many-Body Physics investigates the behavior emerging in complex quantum many-body systems in particular due to the quantum entanglement between its constituents.

Quantum Information is concerned with studying the way in which the laws of quantum mechanics can be used to store and process information and to perform computations. In particular, the possibility of creating superpositions of classical states, and to create correlations without a classical correspondence give rise to a wide range of new phenomena in data processing and computation.

Our research covers a wide range of topics in Quantum Information:

• Entanglement Theory.—Entanglement – correlations between particles which cannot be explained classically – is arguably the most peculiar feature of quantum physics. We work on the classification of the possible types of entanglement in different setups, its quantification in operationally meaningful ways, and its use as a resource for different physical tasks.
• Quantum Algorithms.—Quantum computers hold the promise to outperform classical computers by using quantum superpositions. We study how quantum computers and simulators can be used for the solution of quantum mechanical problems in condensed matter, quantum chemistry, and high-energy physics, and explore ways in which intermediate-scale near-term quantum devices can offer an advantage over classical computers.
• Foundations of quantum mechanics.—We develop fundamental tests of quantum mechanics which allow to distinguish from classical theories (so-called "local hidden variable models"), and study the perspective offered by quantum theory on other fundamental theories such as thermodynamics.

Atoms and light lie at the basis of most of the methods that are used to store, process and transmit quantum information, and the ideas developed in that field are now being implemented in other platforms. Additionally, with the development of new scenarios that combine different technologies, theoretical quantum optics is confronted with new challenges, and the possibility of discovering new phenomena.

Among other, the Theory Division is carrying out research in different topics, some of them in close collaboration with experimentalists:

• Quantum emitters in non-conventional baths.—When atoms or other kind of light emitters are coupled to photonic crystals they experience a wide range of phenomena, like novel ways of sub- and superradiance, effective and exotic long-range interactions, or self-organization. We develop new theoretical methods to describe those systems, and investigate some of those new phenomena.
• Quantum simulation.—We develop methods to use different systems (for instance, atoms, ions, or electrons) to emulate the physics of condensed matter or high-energy physics models. Some of those models are very hard to solve due to the exponential growth in the computational and memory resources with the number of entities involved.
• Quantum devices.—We investigate ways of building different devices to process and transmit quantum information. Those include quantum photon sources, quantum repeaters, or quantum computers. We use different setups, like trapped ions, cavity QED, or electrons in surface acoustic waves.

Systems composed of multiple quantum components exhibit rich physical phenomena and can give rise to the most interesting macroscopic properties (e.g. high-temperature superconductivity or thermalization). Most such systems are very hard to solve, and it is of fundamental interest to develop techniques that allow us a better understanding of these phenomena.

The Theory Division investigates these problems from different perspectives:

• Theoretical aspects: Tensor network theory.—Tensor Networks offer the possibility to construct states where collective properties are determined from small local tensors. One of the goals of the Division is to develop the analytical theory of TNS and achieve an efficient description/understanding of the relevant physical states.
• Non-Gaussian states.—We develop theories and variational ansatzes for bosonic and fermionic systems that extends Gaussian states to interacting systems.
• Numerical/methodological aspects.—Combining Tensor Network with other numerical techniques (e.g. Monte Carlo sampling, machine learning methods), new numerical algorithms are designed that allow us to tackle the most challenging problems.
• Applications to problems in different areas.—We apply the new methods to physically interesting problems, which are hard to approach with other techniques. Examples include models in high energy physics (lattice gauge theories) and strongly correlated quantum systems in more than one spatial dimension.