Springe direkt zu Inhalt

Research

Bulk and boundary bipartition in a holographic tensor-network code.

Bulk and boundary bipartition in a holographic tensor-network code.
Image Credit: Graphics by A. Jahn.

Our group combines ideas of quantum information and high-energy theory to push boundaries in both fields.

The fields of quantum information and high-energy theory are superficially very different: Quantum information is one of the newest branches of theoretical physics, motivated in large part by practical questions of harnessing quantum effects for information processing tasks, with deep roots in classical information theory, condensed matter theory, and quantum optics. High-energy theory, on the other hand, is almost a century old, arguably dating back to Paul Dirac's 1928 paper predicting the positron, and today is concerned both with the theory behind high-energy particle experiments as well as deep questions concerning the unification of quantum field theory with gravity, with entire communities exploring candiates such as string theory.

In recent years, there has been a strong flow of ideas between both fields, in particular applying quantum information ideas to traditional high-energy theory settings. This ranges from longstanding questions of how to define entanglement and subalgebras in quantum field theory to very new developments, such as those involving the relationship between holographic dualities and quantum information and computation. Our group is studying this broad field from many different angles, ranging from mathematical (e.g. algebraic) techniques to concrete many-body models, such as those expressed by tensor networks. These are some of the directions we explore:

Holographic tensor network models. In the past 25 years, there has been an enormous amount of research into holographic dualities, most famously realized by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence introduced in work by Juan Maldacena and Edward Witten, relating gravitational and quantum theories in new and unexpected ways. To understand these dualities better, one can create discretized models of qubits that capture (some of) their properties. A particularly popular approach involves tensor networks, which are ansätze for quantum states that express the geometry of their many-body entanglement in terms of a graph. Tensor networks with hyperbolic geometry can express the "bulk" side of holographic dualities through degrees of freedoms on these graphs while a quantum state is described on its "boundary". Holography-inspired tensor networks are potentially useful ansatz classes to describe CFT states, but can also shed light on the way entanglement and correlations appear in holographic states, such as realizing a discrete version of the Ryu-Takayanagi formula for holographic entanglement entropy.

Holographic codes. Holographic dualities are also related to quantum computation theory, as their bulk/boundary maps can be understood as specific quantum error-correcting codes. In particular, the locality of information within a gravitational bulk theory and that of its dual boundary theory are not equivalent, with local bulk operators encoded as non-local and redundant (and hence error-correctable) boundary operators. An excellent introduction to these topics is given by a set of lectures by Daniel Harlow. Expressing holographic dualities in the language of quantum error correction allows us to both learn more about holography as well as construct holographic code models that may have practical usefulness in future quantum computing platforms. Model of holographic codes can also be expressed using tensor networks, an approach which we discuss in detail in this review paper.

Algebras in quantum field theory and quantum gravity. Many concepts that appear simple in systems of spins and qubits become highly nontrivial in quantum field theory. One such concept is entanglement, which has many clear definitions for qubit systems whose operational meaning is well understood. However, in continuum quantum field theory every subregion has an infinite amount of entanglement with its exterior, as entangled modes appear on arbitarily small length scales. A language for addressing quantum-mechanical operators in such a setting is given by von Neumann algebras, going back to work by John von Neumann and Francis Murray in the 1930s and 40s. Yet, it was understood until recently that many definitions of entanglement measures become useless in continuum QFT. However, it now appears as though the inclusion of even perturbative gravitational corrections modifies the algebras of subregions such that some entanglement measures are again well-defined. However, a remaining challenge is to understand how such algebras can be expressed in full quantum gravity. A good popular-science introduction to this very new subfield is given in this article by Quanta Magazine, while a more rigorous introduction to von Neumann algebras in QFT is given in these notes by Jonathan Sorce.