Applications of Quantum Information in QFT and Cosmology

Detailed Program for Applications of Quantum Information in QFT and Cosmology

Rob Myers, Perimeter Institute

Video

Title: Complexity, Holography & Quantum Field Theory

Abstract:

Complexity is a natural concept in computer science and quantum information science. Recently it was suggested that complexity is also a useful notion to characterize states in quantum field theory and in holographic descriptions of quantum gravity. My talk will review these ideas as well as discuss some recent developments in holographic complexity.

Shira Chapman, Ben-Gurion University

Video

Title: Holographic Complexity and de Sitter Space

Abstract:

I will discuss the complexity=volume conjecture in double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. I will comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon. This is based on work with Damian Galante and Eric David Kramer.

Michal Heller, Max Planck Institute, AEI, Potsdam

Video

Title: Towards deriving a gravity dual to complexity

Abstract:

What are boundary interpretations of holographic complexity proposals and what are gravity duals to complexity are important open questions. I will discuss two ongoing efforts to answer them, which are based on searching for a gravity dual of a circuit cost and, through minimization of the latter object, to a gravity dual of bona fide complexity. Based on 2101.01185 and an ongoing work.

Javier Magan, University of Pennsylvania

Video

Title: Completeness in QFT, holography, and the charged density of states

Abstract:

We describe a general notion of completeness in QFT. It asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this completeness principle such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. For non-complete theories, we explain how the existence of generalized symmetries is unavoidable, and further, that they always come in dual pairs with precisely the same "size" Using this new understanding, we argue against the existence of generalized symmetries in the bulk of holographic theories, and prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT.

Ying Zhao, KITP, UCSB

Video

Title: Quantum circuit and matter collisions in the black hole interior

Abstract:

The Schwarzschild wormhole has been interpreted as an entangled state. If Alice and Bob fall into each of the black hole, they can meet in the interior. We interpret this meeting in terms of the quantum circuit that prepares the entangled state. Alice and Bob create growing perturbations in the circuit, and we argue that the overlap of these perturbations represents their meeting. We identify the post-collision region as the region storing the gates that are not affected by any of the perturbations. We use this picture to analyze how the post-collision region shrinks after strong collisions between two localized shocks and compare it with estimated result from general relativity. We see that there is a boundary mechanism with which bulk matter gravitationally interact in the interior: perturbations overlapping in one shared quantum circuit. The same mechanism applies no matter the colliding signals come from the same boundary or different non-interacting boundaries.

Koji Hashimoto, Kyoto University

Video

Title: An energy bound on chaos

Abstract:

We conjecture an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and quantum field theories. The conjecture states that the Lyapunov exponent as a function of the total energy grows no faster than linearly in the energy, in the high energy limit, under plausible physical conditions on the Hamiltonian. To the best of our knowledge this chaos energy bound is satisfied by any classically chaotic Hamiltonian system known. We provide arguments supporting the conjecture for generic classically chaotic billiards and multi-particle systems.

Vijay Balasubramanian, University of Pennsylvania

Video

Title: Quantum Complexity, Integrability, and Chaos

Abstract:

The states of quantum systems grow in complexity over time as entanglement spreads between degrees of freedom. Following ideas in computer science, we formulate the complexity of evolution as the length of the shortest geodesic on the unitary group manifold between the identity and the time evolution operator, and use the SYK family of models with N fermions to study this quantity in free, integrable, and chaotic systems. In all cases, the complexity initially grows linearly in time, and the shortest path lies along the physical time evolution. This linear growth is eventually truncated by "shortcuts" on the unitary manifold that are shorter than the physical time evolution. We explicitly locate such shortcuts and hence show that in the free theory, shortcuts occur at a time of O(N^1/2), truncating complexity growth at this scale. We also find an explicit operator which "fast-forwards" time evolution with this complexity. In a class of integrable theories, we show that shortcuts appear in a time upper bounded by O(poly(N)), again truncating complexity growth. Finally, in chaotic theories we argue that shortcuts do not occur until exponential times, after which it becomes possible to find infinitesimally nearby fixed-complexity approximations to the time evolution operator. We relate these results to the Eigenstate Complexity Hypothesis, a new criterion on the spectrum of energy eigenstates that guarantees an exponential increase of complexity over time that is consistent with maximal chaos.

Johanna Erdmenger, Julius-Maximilians-University, Würzburg

Video

Title: Relating quantum information aspects of quantum mechanics and gravity

Abstract:

I will present two recent works of our Wuerzburg group on this subject. The first one is devoted to extending the Nielsen geometric approach operator complexity to the SU(N) group and considering the large N limit. This is motivated by the aim of constructing a gravity dual for computational complexity. We implement the Euler-Arnold approach to identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory for the evaluation of operator complexity for large qudits. I will discuss the ergodicity properties of our result. Second, I will present a relation between entanglement in simple quantum mechanical qubit systems and in wormhole physics as considered in the context of the AdS/CFT correspondence. In both cases, states with the same entanglement structure, indistinguishable by any local measurement, nevertheless are characterized by a different Berry phase. This feature is experimentally accessible in coupled qubit systems. I will also give a group-theory argument highlighting the different factorisation properties of the two-qubit system and the wormhole. Based on 2109.01152 and 2109.06190

S. Prem Kumar, Swansea University

Video

Title: Entanglement evolution, islands, and BCFT

Abstract:

In this talk I will describe aspects of island saddles that contribute to time evolution of measures of entanglement in the Hawking radiation emitted by slowly evaporating black holes (coupled to nongravitating radiation baths). In the adiabatic limit (multiple) island saddles can be identified via a simple prescription in terms of the images of islands in the stream of the Hawking radiation. I will describe how quantum extremal surfaces and the island prescription applied to the JT gravity framework reproduces intricate features of entropy evolution in free fermion BCFT.

Tom Hartman, Cornell University

Video

Title: Entanglement islands in cosmology

Abstract:

I will summarize recent developments on the information paradox involving 'islands' and replica wormholes, and discuss the extent to which these ideas can be applied to cosmology. Three simple rules for island hunting lead to the conclusion that among standard FRW cosmologies, only crunching universes have an island effect. More exotic scenarios, including bubble nucleation and two-dimensional cosmologies, may support islands, but their interpretation is not yet clear.

Bartolmiej Czech, Tsinghua University

Video

Title: Holographic cone of average entropies

Abstract:

The holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to 5 regions. I point out that average entropies of p-partite subsystems can be similarly analysed for arbitrarily many regions. I conjecture that this holographic cone of average entropies is simplicial, and give the exact (conjectured) form of its bounding inequalities and extremal rays. In a certain precise sense, the conjecture explains the composition of almost all known valid holographic inequalities in terms of how many p-partite entropies they feature, and predicts such a composition for many inequalities yet to be discovered. I sketch an interpretation in terms of the holographic Renormalization Group, the erasure correcting capacity of the boundary-to-bulk map, and black hole evaporation.

Discussion

Video

Moderated by Saurya Das, University of Lethbridge and Shajid Haque, University of Cape Town

Panelists:

• Lars Aalsma, University of Wisconsin-Madison

• Vijay Balasubramanian, University of Pennsylvania

• Tom Hartman, Cornell University

Vincent Vennin, APC, Paris

Video

Title: Can we prove that cosmic structures are of quantum mechanical origin?

Abstract:

In the early universe, quantum vacuum fluctuations are amplified and stretched to large distances, giving rise to cosmological over-densities that seed the large-scale structure of our universe. However, astronomers usually analyse the data with purely classical techniques and apparently never need to rely on the quantum formalism to understand them. So are there observational signatures of the quantum origins of primordial perturbations? Can inflation be used to test fundamental aspects of quantum mechanics itself?

Beni Yoshida, Perimeter Institute

Video

Title: Decoding the Entanglement Structure of Monitored Quantum Circuits

Abstract:

Given an output wavefunction of a monitored quantum circuit consisting of both unitary gates and projective measurements, we ask whether two complementary subsystems are entangled or not. For Clifford circuits, we find that this question can be mapped to a certain classical error-correction problem where various entanglement measures can be explicitly computed from the recoverability. The dual classical code is constructed from spacetime patterns of out-of-time ordered correlation functions among local operators and measured Pauli operators in the past, suggesting that the volume-law entanglement in a monitored circuit emerges from quantum information scrambling, namely the growth of local operators. We also present a method of verifying quantum entanglement by providing a simple deterministic entanglement distillation algorithm, which can be interpreted as decoding of the dual classical code. Discussions on coding properties of a monitored Clifford circuit, including explicit constructions of logical and stabilizer operators, are also presented. Applications of our framework to various physical questions, including non-Clifford systems, are discussed as well. Namely, we argue that the entanglement structure of a monitored quantum circuit in the volume-law phase is largely independent of the initial states and past measurement outcomes except recent ones, due to the decoupling phenomena from scrambling dynamics, up to a certain polynomial length scale which can be identified as the code distance of the circuit. We also derive a general relation between the code distance and the sub-leading contribution to the volume-law entanglement entropy. Applications of these results to black hole physics are discussed as well.

Nick Hunter-Jones, Stanford University

Video

Title: Quantum complexity and the long-time behavior of chaotic quantum systems

Abstract:

The quantum complexity of a unitary or state is defined as the size of the shortest quantum computation that implements the unitary or prepares the state. The notion has far-reaching implications spanning computer science, quantum many-body physics, and high energy theory. Complexity growth in time is a phenomenon expected to occur in holographic theories and strongly-interacting many-body systems more generally, but proving anything about the complexity of a state or unitary is notoriously difficult. By considering ensembles of systems, and using tools from quantum information theory, we will prove statements about complexity growth, saturation, and recurrence in various models, specifically focusing on random quantum circuits (a simple model of local chaotic dynamics).

Shinsei Ryu, Princeton University

Video

Title: Multipartitioning topological phases and quantum entanglement

Abstract:

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.