Entanglement in Quantum Fields

IWH Heidelberg (Germany) + online

IWH Heidelberg (Germany) + online

Internationales Wissenschaftsforum Heidelberg Hauptstrasse 242 D-69117 Heidelberg


While quantum field theory is the framework to describe almost all phenomena in fundamental physics, its quantum information theoretic aspects remain poorly understood. It is conceivable that an improved understanding allows to formulate a much more detailed theory for quantum systems out-of-equilibrium than available to date. On the other side, quantum simulation experiments with ultracold atomic gases allow to emulate quantum field theories in synthetic quantum systems and may be used to investigate quantum information theoretic aspects.

The workshop on Entanglement in Quantum Fields (EQF2021), June 28-30, brings together experts on quantum information theoretic aspects of quantum fields with researchers on ultracold atomic quantum gases with the aim of 

  • Devising settings in which quantum simulators can be applied to QFT problems
  • Developing new tools for experimentally detecting and quantifying entanglement
  • Integrating quantum information concepts in quantum field theoretical descriptions

Keynote talks will provide an introduction and overview on the different aspects with the aim of providing a basis for initiating discussions between the different communities. Shorter invited talks are dedicated to recent progress on specific topics. Abundant discussion time is foreseen for the vital interactions between experimental and theoretical physicists working in the different areas.

This workshop will be held as a hybrid event with a limited number of participants being physically present at IWH and the possibility to join virtually via zoom. Speakers and participants may indicate their preference on in person or virtual attendance. As of now, all the participants who indicated that they would like to attend in person, can do so. Participants who would like to apply for financial support for travel expenses should contact Tina Kuka (t.kuka@thphys.uni-heidelberg.de) for more information.

Keynote Speakers

Marcus Huber (IQOQI Vienna)
Peter Zoller had to cancel due to illness and will be replaced by Christian Kokail and Andreas Elben (University of Innsbruck & IQOQI)
J. Ignacio Cirac (MPQ)
Otfried Gühne (Siegen University)
Johanna Erdmenger (Würzburg University)
Pasquale Calabrese (SISSA)


Stefan Floerchinger
Martin Gärttner
Helmut Strobel

Entanglement in Quantum Fields is supported by the DFG funded collaborative research center ISOQUANT (SFB 1225)                         

  • Adrian Aasen
  • Adrian Braemer
  • Albert Gasull
  • Alexander Rothkopf
  • Andreas Elben
  • Andreas Ketterer
  • Aniket Rath
  • Ayaka Usui
  • Benjamin Schiffer
  • Benoit Vermersch
  • Bjarne Bergh
  • Christian Kokail
  • Daniel Malz
  • David Horvath
  • Giacomo Bighin
  • Giuseppe Di Giulio
  • Giuseppe Vitagliano
  • Guillem Müller
  • Guoxian Su
  • H. Chau Nguyen
  • Henrik Müller-Groeling
  • Hui Sun
  • Ignacio Cirac
  • Iliya Esin
  • Irénée Frérot
  • Ivan Kukuljan
  • James Schneeloch
  • Jan Dreher
  • Jean-Daniel Bancal
  • Ji-Yao Chen
  • Jianshun Gao
  • Johanna Erdmenger
  • Jordi Tura i Brugués
  • Kevin Grosvenor
  • Kiara Hansenne
  • Konstantinos Sfairopoulos
  • Lata Kharkwal Joshi
  • Luca Capizzi
  • Manuel Gessner
  • Marcus Huber
  • Marek Gluza
  • Markus Reinig
  • Markus Schröfl
  • Marti Carmen Bañulus
  • Marvin Holten
  • Matteo Fadel
  • Matteo Votto
  • Maximilian Hartmann
  • Maximilian Kramer
  • Maximilian Müllenbach
  • Mira Sharma
  • Mireia Tolosa
  • Mohammadamin Tajik
  • Natalia Sánchez-Kuntz
  • Nicolai Friis
  • Niklas Euler
  • Nikolai Wyderka
  • Oliver Stockdale
  • Otfried Gühne
  • Pasquale Calabrese
  • Patrick Andriolo
  • Philipp Kunkel
  • Philipp Lunt
  • Philipp Preiss
  • Philipp Schüttelkopf
  • Piero Naldesi
  • Pim van den Heuvel
  • Riccarda Bonsignori
  • Robert Jonsson
  • Robert Ott
  • Rohan Srikumar
  • Sara Ditsch
  • Sara Murciano
  • Satoya Imai
  • Shachar Fraenkel
  • Sidiney Bruno Montanhano
  • Skyler Degenkolb
  • Sophia Lahs
  • Sophie Rohletter
  • Spyros Sotiriadis
  • Stefan Lannig
  • Steven Bass
  • Thomas Poulis
  • TIlman Enss
  • Tobi Haas
  • Xhek Turkeshi
  • Xiao-Dong Yu
  • Yash Gurbani
  • Yi Lu
  • Yue Zhang
  • Yunxin Ye
  • Zhaoyu Zhou
  • Zheng Gong
  • Zoltán Kolarovszki
    • 1
    • Monday Morning
      • 2
        Lecture: Tensor Networks and Quantum Field Theories

        Certain Quantum Many-body states defined on lattices can be efficiently described in terms of tensor networks. Those include Matrix Product States (MPS), Projected Entangled-Pair States (PEPS), or the Multi-scale Entanglement Renormalization Ansatz. They play an important role in quantum computing, error correction, or the description of topological order in condensed matter physics, and are widely used in computational physics. In the last years,
        it has also been realized their suitability to describe Lattice Gauge Theories, at least in low dimensions. In this talk I will review some of the basic ideas about tensor networks and their applications to lattice gauge theories, and explain current efforts to extend them to higher dimensions and to the continuum limit.

        Speaker: J. Ignacio Cirac (MPQ Garching)
      • 10:30 AM
        Coffee break
      • 3
        TNS for lattice gauge theories: numerical strategies beyond 1D

        In the last years, the suitability of tensor network states for the study of one-dimensional gauge theories has been established: it is possible to conduct numerical studies of lattice gauge theories (LGT) using TNS that enable precise continuum extrapolations in very different setups, including finite density scenarios, where traditional Monte Carlo approaches fail. A similar systematic study in two dimensions becomes much more challenging, due to increased computational costs, but also to the presence of plaquette terms. With a newly developed update strategy it is nevertheless possible to treat these terms efficiently, as we have demonstrated with the first ab initio iPEPS study of a LGT (Z3) in 2+1 dimensions.
        Additionally, other recently introduced numerical TNS techniques that target properties of the models at finite energy density or temperature can be applied to LGT problems, and provide new handles to their physical properties.

        Speaker: Mari Carmen Bañulus (MPQ Garching)
      • 4
        Certificates of many-body properties assisted by machine learning

        Computationally intractable tasks are ubiquitous in physics and optimization . Whereas variational approaches count amongst the most direct tools to find an optimal solution, they suffer from two main drawbacks: (i) non-convexity of the cost function and/or the feasible set and (ii) they provide only an inner bound to the optimal solution. On the other hand, relaxation techniques, which allow for more efficient methods, provide outer bounds to the optimal solution. Hence, the combination of both, variational ansatze and relaxations, provide bounded intervals which contain the optimal solution, thus allowing for control of the optimization error. We propose a novel approach combining the power of relaxation techniques with deep reinforcement learning (RL) to find the best possible relaxations given a limited computational budget. In many cases of interest, given an optimization problem, we consider a set of constraints that must be fulfilled by the solution. We can solve the resulting constrained optimization problem through semidefinite programming (SdP). Relaxing the constraints simplifies the problem, but it may yield looser bounds. At the same time, some smart relaxations may yield better bounds than others while using similar computational resources. Hence, it is paramount to find the best trade-off between accuracy and simplicity. Nevertheless, a successful search often relies upon specific insight about the problem at hand. Conversely, the analysis of an efficient proof is likely to reveal useful insight about the system's properties. We propose a systematic method to search for optimal sets of constraints given a computational budget. We illustrate the procedure in the context of ground state energy approximation. We showcase its validity in various scenarios where the ground states have different properties. Additionally, we benchmark the results against other optimization techniques and we study the effect of transfer learning. We highlight that our methods, while presented in the context of ground state energy approximation, are actually of much broader applicability, ranging, e.g. from entanglement witnesses optimization to device-independent quantum information processing tasks.

        Speaker: Jordi Tura (Leiden University)
      • 5
        Interaction as a UV-regulator for entanglement in Bose-Einstein condensates.

        The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a non-relativistic quantum field theory in the vacuum limit, and we show that the latter has vanishing entanglement. In the opposite limit of a region that is large compared to the healing length, the entanglement entropy is like in the vacuum of a relativistic theory where the velocity of light is replaced with the velocity of sound and where the inverse healing length provides a natural ultraviolet regularization scale. We show these results, by calculating the von Neumann and Rényi entanglement entropies for a one-dimensional quasi-condensate.

        Speaker: Natalia Sanchez Kuntz (Heidelberg University)
    • 12:30 PM
      Lunch break
    • Monday Afternoon
      • 6
        Lecture: Entanglement beyond qubits

        Entanglement can be considered the key resource behind many applications of quantum information processing, as well as critical for the foundation of thermodynamics and the emergence of a classical world. While the simplest applications can be sufficiently addressed with the, now relatively well understood, entanglement of two qubits, more complex notions of entanglement hold huge potential for improving those simple protocols and are required for an understanding of complex phenomena in many-body physics.
        In this talk I will give a general overview of entanglement beyond the simple two qubit case, from multipartite to multi-dimensional entanglement and showcase a couple of recent applications for higher-dimensional encoding of quantum information in photonic protocols.

        Speaker: Marcus Huber (Vienna University)
      • 3:30 PM
        Coffee break
      • 7
        The Entanglement-Correlation Connection: Entropic workarounds to cutting-edge quantum characterization

        This talk focuses on the relationship between the correlations we can measure between quantum objects, and the entanglement shared by them. In particular, we show how these correlations can be used to quantify (not just qualify) both bipartite and genuine multipartite entanglement, and show how the uncertainty principle fundamentally alters the relationship between correlation and entanglement in the multi-partite regime. In addition, we illustrate how entropic measures of correlation and uncertainty offer exceptional advantages in the efficient characterization of correlations and entanglement.

        Speaker: James Schneeloch (Air Force Research Laboratory, Rome, NY)
      • 8
        Lower bounding entanglement in quantum many-body systems using entropic uncertainty relations

        Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental questions, e.g., in quantum statistical mechanics and condensed-matter physics. At the same time it poses a significant challenge because the evaluation of entanglement measures typically requires the full reconstruction of the quantum state, which is extremely costly in terms of measurement statistics. We derive an improved entanglement bound for bipartite systems, which requires measuring joint probability distributions in only two different measurement settings per subsystem, and demonstrate its power by applying it to currently operational experimental setups for quantum simulation with cold atoms.

        Speaker: Bjarne Bergh (University of Cambridge)
      • 9
        Tomography and non-equilibrium dynamics in a continuous field quantum simulator

        Atom chips allow to manipulate the low-energy effective field theory of individual or coupled one-dimensional gases. I will present recent direct observations of coherent wave-packet propagation within an effective light cone following a global quantum quench from effectively the Klein-Gordon regime to a Tomonaga-Luttinger liquid. These experimental developments are particularly appealing as they allow to gain an understanding of the physics of the system comparable to that obtained by theoretical computations and it will be my aim to show that in an illustrative way. The fact that direct experimental observations can match closely the most instructive theoretical observables hints at one possible way quantum simulation technology may come into play in future physics research. I will also tell you how we do tomography of the phononic fluctuations based on matter-wave interferometry using data from non-equilibrium quenches and mention our ongoing work towards using such reconstructions to decide whether the locally propagating correlation fronts entail bipartite entanglement. The research presented was motivated by our recent studies of the decay and revival of non-Gaussian correlations and our proposal for building quantum field machines using the digital-mirror-device control available on the atom chip.

        Speaker: Marek Gluza (FU Berlin)
    • Tuesday Morning
      • 10
        Lecture: Characterizing Quantum Many-Body States via Entanglement Hamiltonian Tomography

        The experimental characterization and quantification of entanglement properties, and the entanglement spectrum in particular, play a major role in our understanding of modern quantum many body physics in the lab. For most quantum lattice systems of interest, the reduced density matrix ρ of the lattice is described by a thermal state of a quasi-local Entanglement Hamiltonian H: ρ = exp(-β H). As a I will show in this talk, the parametrization of the reduced density matrix in terms of the Entanglement Hamiltonian allows for the determination of entanglement properties like the Schmidt-decomposition with a drastically reduced number of experimental runs. For ground states of a many-body systems, an efficient parametrization is suggested by the Bisognano-Wichmann theorem of axiomatic field theory, while for quantum quenches to a critical point an ansatz is provided by conformal field theory. Finally, I will discuss efficient quantum protocols to determine the Entanglement Hamiltonian whose properties can be investigated on the quantum device without any additional classical post-processing steps.

        Speaker: Christian Kokail and Andreas Elben (Innsbruck University)
      • 10:30 AM
      • 11
        Correlations and Entanglement in Microscopic Samples of Ultracold Fermions

        Ultracold gases are synthetic quantum systems that are exceptionally well suited for the study of strongly interacting fermions.On the one hand, ultracold Fermi gases naturally exhibit pairing,superfluidity and collective excitations known from solid state physics. On the other hand, their implementation in the laboratory allows microscopically resolved observations down to the single-particle level.This combination enables the application of concepts from quantum information theory to condensed matter-like systems. In this talk, I will discuss our recent experimental progress in detecting correlations and entanglement in fermionic few-body systems realized with Lithium 6 in optical tweezers. Using the AMO toolbox, systems with deterministically controlled particle number can be prepared in a specific quantum state and be interrogated through single particle-resolved imaging in momentum space. I will discuss how such probes can reveal coherences and entanglement in a simple dimer through a reconstruction of the density matrix. In our most recent experiments, we have achieved full control over systems with more than ten particles in two dimensions, where methods based on the density matrix are no longer tractable. I will discuss ideas on how to detect and interpret correlations for such challenging system sizes.

        Speaker: Philipp Preiss (Heidelberg University)
      • 12
        Activation of genuine multipartite entanglement: beyond the single-copy paradigm of entanglement characterisation

        Entanglement shared among multiple parties presents complex challenges for the characterisation of different types of entanglement. One of the most basic insights is the fact that some mixed states can feature entanglement across every possible bipartition of a multipartite system, yet can be biseparable, i.e., can be produced via a mixture of partially separable states. To distinguish biseparable states from those states that genuinely cannot be produced from mixing partially separable states, the term genuine multipartite entanglement was coined. The premise for this distinction is that only a single copy of the state is distributed and locally acted upon. However, advances in quantum technologies prompt the question of how this picture changes when multiple copies of the same state become locally accessible. Here we show that multiple copies unlock genuine multipartite entanglement from partially separable states, even from undistillable ensembles, and we demonstrate that more than two copies can be required to observe this effect.
        Our results show that a modern theory of entanglement in multipartite systems, which includes the potential to locally process multiple copies of distributed quantum states, exhibits a rich structure that goes beyond the convex structure of single copies. Indeed, based on our results, we present two conjectures about this structure: (i) the existence of a hierarchy of k-copy activatable states, for which k-1 copies remain biseparable, but k copies are GME, and (ii) the asymptotic collapse of the hierarchy of genuinely k-partite entangled states, i.e., that k copies of any biseparable but not partially separable state become GME as k tends to infinity. In other words, we conjecture separability in multipartite systems to asymptotically collapse to the simple bipartite concept of separability in scenarios with unbounded numbers of copies, and we show that two copies are certainly not sufficient for reaching this simple limit, thus leaving the practical certification a rich problem to be studied.

        Reference: [1] Hayata Yamasaki, Simon Morelli, Markus Miethlinger, Jessica Bavaresco, Nicolai Friis, and Marcus Huber, Activation of genuine multipartite entanglement: beyond the single-copy paradigm of entanglement characterisation, arXiv:2106.01372 [quant-ph] (2021)

        Speaker: Nicolai Friis (Vienna University)
      • 13
        Spin squeezing and entanglement quantification in spin-j atomic gases

        I will present some recent results on entanglement detection and quantification with collective spin measurements in many-body ensembles. After a brief review of the idea of “Spin Squeezing” and its relation with multipartite entanglement and quantum metrology, I will show how the original spin squeezing approach can be generalized in several respects and how it allows to quantify multipartite entanglement by means of the so-called depth of entanglement. Especially, I will present particular examples of criteria that has been recently applied to detect the depth of entanglement in (i) unpolarized Dicke states, produced dynamically in a Rb BEC [1,2]; (ii) Planar Quantum Squeezed states, produced with Quantum-Non-Demolition measurements in a Rb atomic cloud [3]. Similarly, I will present EPR-like criteria tailored to detect bipartite entanglement in generalized spin squeezed states split in two spatially separated modes [4,5], analogous to other well known criteria [6], but applicable to a wider set of states. In the final part, I will focus on the quantification of entanglement by means of entanglement monotones with similar methods [7]. I will consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation (BSA) and the generalized robustness (GR). As a concrete application, I will show the results of applying this method with experimental data of a spin-squeezed Bose-Einstein condensates of 500 atoms.
        [1] B. Lücke, J. Peise, G. Vitagliano, J. Arlt, L. Santos, G. Tóth, and C. Klempt. Detecting multiparticle entanglement of dicke states. Phys. Rev. Lett., 112:155304, 2014.
        [2] G.Vitagliano, I.Apellaniz, M.Kleinmann, B.Lücke, C.Klempt, and G.Toth. Entanglement and extreme spin squeezing of unpolarized states. New J. Phys., 19, 2017.
        [3] G. Vitagliano, G. Colangelo, F. Martin Ciurana, M. W. Mitchell, R. J. Sewell and G. Tóth, Entanglement and extreme planar spin squeezing, Phys. Rev. A 97 020301(R) (2018)
        [4] K. Lange, J. Peise, B. Lücke, I. Kruse, G. Vitagliano, I. Apellaniz, M. Kleinmann, G. Toth, C. Klempt, Entanglement between two spatially separated atomic modes, Science 360 416–418 (2018)
        [5] G. Vitagliano, M. Fadel, I. Apellaniz, M. Kleinmann, B. Lücke, C. Klempt, G.Tóth, Detecting Einstein-Podolsky-Rosen steering and bipartite entanglement in split Dicke states, arXiv:2104.05663
        [6] V. Giovannetti, S. Mancini, D. Vitali, P. Tombesi, Characterizing the entanglement of bipartite quantum systems, Phys. Rev. A 67, 022320 (2003)
        [7] M. Fadel, A. Usui, M. Huber, N. Friis, G. Vitagliano, Entanglement quantification in atomic ensembles, arXiv:2103.15730

        Speaker: Giuseppe Vitagliano (Vienna University)
    • 12:30 PM
    • Tuesday Afternoon
      • 14
        Lecture: Entanglement and symmetry in extended quantum systems

        Entanglement and symmetries are two pillars of modern physics. Surprisingly, only in very recent times the interplay between these two fundamental concepts became the theme of an intense research activity merging together notions and ideas from quantum information, quantum field theory, quantum optics, holography, many-body condensed matter, and many more. In this talk, I will review some of the more interesting findings for symmetry resolved entanglement ranging from purely field theoretical ones to microscopical lattice models for disordered systems. The focus of the talk will be on the results and outlooks rather than on the the technical derivations.

        Speaker: Pasquale Calabrese (SISSA Trieste)
      • 3:30 PM
        Coffee break
      • 15
        Entropic entanglement criteria in phase space

        Typically, entropic uncertainty relations and inseparability criteria are formulated for marginal distributions in phase space. In this talk, I discuss an approach based on the Husimi Q-distribution, which can be measured following the heterodyne detection protocol. The associated entropy, known as the Wehrl entropy, fulfills an entropic uncertainty relation and can be used to construct entanglement witnesses. In particular, I will discuss the Wehrl mutual information, which is a perfect entanglement witness for all pure states, and I will derive a general inseparability criterion based on the Wehrl entropy, which certifies entanglement in previously undetectable regions.

        Speaker: Tobias Haas (Heidelberg University)
      • 16
        Entanglement detection via entropies in spinor Bose gases

        Simultaneous measurements of two non-commuting spin observables allows for direct access to a quasi-probability distribution and its associated entropy. In the Gaussian regime, this corresponds to the Husimi Q-distribution and Wehrl entropy, respectively. We analytically and numerically model the system and measure a non-zero Wehrl mutual information—a perfect entanglement witness for pure states. We present a preliminary analysis of experimental data that shows for certain times non-zero Wehrl mutual information is observed.

        Speaker: Oliver Stockdale (Heidelberg University)
      • 17
        Detecting entanglement with tools from metrology

        The central tool of quantum metrology, the quantum Fisher information (QFI), quantifies the sensitivity of quantum states under small perturbations. Besides identifying strategies to overcome classical precision limits, the QFI provides a versatile tool to detect and quantify multipartite entanglement and steering. We show how the QFI can reveal the structure of inseparable partitions, leading to a detailed characterization of multipartite entanglement beyond entanglement depth and k-separability. Furthermore, the QFI describes a complementarity relation that can be used to formulate the Einstein-Podolsky-Rosen (EPR) paradox in the framework of quantum metrology, leading to a witness for EPR steering. Metrological entanglement witnesses are more powerful than variance-based methods such as Reid's criterion or spin-squeezing coefficients and can be systematically optimized from a limited set of measurable observables.

        Speaker: Manuel Gessner (ENS Paris)
    • Wednesday Morning
      • 18
        Lecture: Characterizing Quantum Correlations with Randomized Measurements

        If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework. Finally, we analyze the resources needed for a statistically significant test

        S. Imai, N Wyderka, A. Ketterer, O. Gühne, Phys. Rev. Lett. 126, 150501 (2021)
        A. Ketterer, S. Imai, N. Wyderka, O. Gühne, arXiv:2012.12176

        Speaker: Ottfried Gühne (Siegen University)
      • 10:30 AM
      • 19
        Statistical physics empowers quantum information: scalable methods for entanglement detection in multipartite systems

        Demonstrating the ability to manipulate quantum-entangled states in scalable multipartite systems represents an important challenge for quantum simulators and computers. Beyond a few tens of qubits, one cannot rely on tomographically-complete information about the prepared quantum state, for at least two reasons: 1) implementing the required measurements might not be currently possible; 2) the number of required measurements, scaling exponentially with the number of qubits, might be unreasonably large. It is therefore crucial to develop methods to probe entanglement from only partial information. Specifically, we will focus on a given set of expectation values for some observables (typically: few-body correlations). Entanglement is then revealed by the violation of a certain entanglement witness by the available data. How can one exhaustively test the capability of a given data set to demonstrate entanglement? Clearly, even if no existing entanglement witness is violated, this does not exclude the possibility that another witness, yet to be discovered, is violated by the same data. In this talk, I will present two complementary approaches to solve this problem in a flexible and scalable way, that is, with a computational cost which scales polynomially with the number of qubits. These approaches are inspired by statistical physics, and take advantage of the classical nature of correlations in separable states. One approach (https://arxiv.org/abs/2101.02038, https://arxiv.org/abs/2004.07796) is a variational search over all separable states, trying to reproduce the data at hand. The failure of this optimization marks the success of entanglement detection. In the second approach, we test positive semidefinite constraints obeyed by the data if they are compatible with a separable state. Both approaches deliver, as an output, a specific entanglement witness violated by the data if the latter cannot be reproduced by a separable state -- providing qualitative insight into the driving mechanism for many-body entanglement. These approaches complement each other, systematically sandwiching the boundary of the convex set defined by separable states, at a scalable computational cost. I will explain these methods, and present results obtained by investigating theoretical many-body states.

        Speaker: Irénée Frérot (ICFO Barcelona)
      • 20
        Entanglement for any definition of two subsystems

        The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a set of states. This talk presents the notion of "absolutely entangled set" of quantum states: sets such that for any possible choice of global basis, at least one of the states in the set is entangled. Such a set has the peculiarity of featuring entanglement for any possible definition of the subsystems. We present a minimum example of this phenomenon, with a set of four states in C^4=C^2⊗C^2. Moreover, we propose a quantitative measure for absolute set entanglement. To lower-bound this quantity, we develop a method based on polynomial optimization to perform convex optimization over unitaries, which is of independent interest.

        Speaker: Jean-Daniel Bancal (Univeristé Paris-Saclay)
      • 21
        Einstein-​Podolsky-Rosen steering as a resource for quantum metrology

        Einstein-​Podolsky-Rosen (EPR) steering is typically revealed from the possibility of predicting the results of non-​commuting measurements with a precision that seems to violate the uncertainty principle. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. In this talk I will present a formulation of the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. We derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-​known uncertainty-​based criteria. Our result identifies useful steering for quantum enhanced precision measurements and allows one to uncover steering of non-​Gaussian states in state-​of-the-art atomic and optical experiments.

        Speaker: Matteo Fadel (Basel University)
    • 12:30 PM
    • Wednesday Afternoon
      • 22
        Lecture: Quantum entanglement and black holes

        Quantum entanglement plays an important role in two seemingly distinct areas of physics: For studying the quantum properties of black holes as well as for quantum information theory. Quantum entanglement and computational complexity may be mapped to geometric quantities. This provides a new link between theoretical concepts for black holes and quantum information. A central role in this context is played by the holographic principle, according to which the information stored in a volume is encoded on its surface, as is the case for black holes. In the talk I will describe the essential new concepts that relate quantum entanglement to geometry and gravity. I will explain how these relations may be used to obtain both a further understanding of quantum black holes, as well as further advances for the theoretical foundations of quantum computing.

        Speaker: Johanna Erdmenger (Würzburg University)
      • 4:00 PM
        Coffee break
      • 23
        Experimental Simultaneous Extraction of Non-Commuting Obervables for Accessing Quantum Correlations in a Spinor Bose-Einstein Condensate

        While entanglement between single pairs of discrete entities like photons, atoms, or ions is routinely implemented and investigated in experiments, the extension to continuous systems is still a challenge on the side of preparation as well as detection. We explore this continuous limit with our experiments employing a quasi-1-dimensional Bose-Einstein condensate of ^{87}Rb which features rich and well understood spin-1 dynamics due to the interatomic interactions. We combine the spatial resolution provided by an in-situ imaging system with a flexible readout scheme for simultaneously extracting multiple non-commuting observables to access different components of the continuous spin field describing our atomic cloud. Therefore, we apply this technique not only to access cross-correlations between different observables to identify the structure of excitations in non-equilibrium systems but we also directly certify entanglement between spatial subsystems. In this talk I will introduce the implementation of this readout scheme and provide an overview of thereby experimentally accessible observables and correlations revealing entanglement.

        Speaker: Stefan Lannig (Heidelberg University)
      • 24
        Programmable Interactions and Emergent Geometries in an Atomic Array

        Interactions form the basis for the experimental generation of entanglement between quantum objects. Typical quantum simulation platforms such as atomic systems or trapped ions feature local interactions which decay as a function of distance. The spatial entanglement structure that can be generated is thus inherently connected to the physical geometry of the system. In this talk, I will present the recent results of our experiment where we use an optical cavity to mediate programmable long-range interactions between a 1D array of atomic ensembles. By tailoring the frequency spectrum of a drive field we achieve arbitrary control over the distance dependence of the interactions as well as their relative sign. This allows us to implement dynamics in various effective geometries which are entirely distinct from the physical arrangement of the atoms, including frustrated 2D lattices and an emergent tree-like geometry inspired by holographic models of quantum gravity. We demonstrate this by directly reconstructing the geometry from the measured spin correlations. In the realm of quantum information, these new capabilities pave the way towards engineering quantum states with specific spatial entanglement structure for quantum sensing and quantum computation.

        Speaker: Philipp Kunkel (Stanford University)