Quantum Information Entropy in Physics

Timetable of the workshop

• Green and red colors indicate tutorial and invited talks, respectively.
• All talks, except explicitly specified, should be given in English.
• All slots include the time for questions.

March 21 (Monday)

• 12:20-   Opening remarks


• 12:30-14:00   Francesco Buscemi (Nagoya U.)

  A walk through the zoo of quantum information entropies
  In this tutorial we will take a look at some of the most useful measures of "statistical distinguishability" in quantum theory, their properties, and their use in various information-theoretic settings, focusing, in particular, on the property of "monotonicity". The latter, epitomized by various direct and reverse data-processing theorems (or "quantum Blackwell theorems"), provides the information-theoretic backbone of many recent progresses in generalized resource theories.

• 14:15-15:15   Takahiro Sagawa (U. Tokyo)

  An introduction to resource theory of thermodynamics
  Resource theory is an information-theoretic framework to quantify "useful resources" and has attracted much attention in terms of quantum thermodynamics [1]. In this talk, I will present a short introduction to resource theory of thermodynamics, by focusing on some fundamental properties of quantum entropies, divergences, and state convertibility. I will also talk about asymptotic theory based on information spectrum beyond i.i.d. situations, and discuss our resent result about the existence of complete thermodynamic potential for ergodic many-body systems [2,3].
  
  [1] T. Sagawa, "Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics", SpringerBriefs in Mathematical Physics (2022). arXiv:2007.09974
  [2] P. Faist, T. Sagawa, K. Kato, H. Nagaoka, F. Brandao, Phys. Rev. Lett. 123, 250601 (2019).
  [3] T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, F. Brandao, J. Phys. A: Math. Theor. 54, 495303 (2021).

• 15:30-16:30   Tadashi Takayanagi (Kyoto U.)

  Holography and Quantum Entanglement
  The idea of holography in string theory provides a simple geometric computation of entanglement entropy. This generalizes the well-known Bekenstein-Hawking formula of black hole entropy and strongly suggests that a gravitational spacetime consists of many bits of quantum entanglement. In this tutorial, I will explain basic aspects of this connection between holography and quantum entanglement. Later I will also briefly explain recent developments of holographic entanglement related to Page curves in black hole information problem.

• 16:45-17:45   Shunsuke Furukawa (Keio U.)

  Quantum entanglement in topological phases and symmetry-broken phases
  I will review some applications of entanglement entropy (EE) and entanglement spectra (ES) in quantum many-body systems. In a variety of topological phases, it has been found that the ES has a similar structure as the edge-mode spectrum. The "cut and glue" picture gives a physical explanation of this remarkable entanglement-edge correspondence [1]. I will explain a simple formulation of this picture based on two coupled (chiral) Tomonaga-Luttinger liquids [2]. The obtained ES can be used to derive the so-called topological entropy. In systems with continuous symmetry breaking, the EE shows a subleading logarithmic term whose coefficient is related to the number of Nambu-Goldstone modes [3]. Furthermore, the ES shows a "tower of states" structure reminiscent of the finite-size energy spectrum. I will explain the emergence of analogous features in the intercomponent entanglement in binary Bose-Einstein condensates [4].
  
  [1] X.-L. Qi, H. Katsura, and A.W.W. Ludwig, Phys. Rev. Lett. 108, 196402 (2012).
  [2] R. Lundgren, Y. Fuji, S. Furukawa, and M. Oshikawa, Phys. Rev. B 88, 245137 (2013).
  [3] M. A. Metlitski and T. Grover, arXiv:1112.5166.
  [4] T. Yoshino, S. Furukawa, and M. Ueda, Phys. Rev. A 103, 043321 (2021).

March 22 (Tuesday)

• 9:00-10:00   (Invited) David Huse (Princeton U.)

  Many-body localization: “avalanches” and long-range resonances
  I will review our current understanding (and lack thereof) of the dynamic phase diagram of models of many-body localization (MBL) in one-dimensional systems with quenched randomness and with only short-range interactions. The phase transition out of the MBL phase is believed to be due to the so-called avalanche instability. We now have quantitative new bounds from numerics on the coupling at this phase transition. This reveals that a large portion of the phase diagram is occupied by an intermediate regime where systems of numerically and experimentally accessible sizes and times act in most respects MBL, even though they will instead thermalize in the thermodynamic and infinite time limit. A partial understanding of this phase diagram in terms of long- range many-body resonances will be discussed.
  Reference: Morningstar, et al., arXiv:2107.05642.

• 10:15-11:15   (Invited) Li Gao (Texas U.)

  Approximate Recoverability via Sandwiched Renyi relative entropy
  Data processing inequality (DPI) is a fundamental inequality in quantum information theory. In recent years, starting from the seminal work by Fawzi and Renner, much progress has been made on refining the data processing inequality with a recovery term, which measures the approximate recoverability of input states via the Petz recovery map and its variants. In this talk, I will present some progress on approximate recoverability via sandwiched R\'enyi relative entropy. This talk is based on a joint work with Mark Wilde.

• 11:30-12:00   Yuya Kusuki (Caltech)

  Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
  Recently, boundary conformal field theories (BCFTs) have attracted much attention in the context of quantum gravity. This is because a BCFT can be dual to gravity coupled to a heat bath CFT, known as the island model. On this background, it would be interesting to explore the duality between the boundary and the braneworld. However, this seems to be a challenging problem. The reason is because although there has been much study of rational BCFTs, there has been comparatively little study of irrational BCFTs, and irrational BCFTs are expected to be the boundary duals of the braneworlds. For this reason, we explore properties of boundary ingredients: the boundary primary spectrum, the boundary-boundary-boundary OPE coefficients and the bulk-boundary OPE coefficients. For this purpose, the conformal bootstrap is extremely useful. This is the first step in providing an understanding of BCFTs in the context of braneworld holography by using the conformal bootstrap. The techniques developed in this paper may be useful for further investigation of irrational BCFTs.

• 13:30-14:00   Satoshi Yoshida (U. Tokyo)

  Universal construction of decoders from encoding black boxes
  Isometry operations encode the quantum information of the input system to a larger output system, while the corresponding decoding operation would be an inverse operation of the encoding isometry operation. Given an encoding operation as a black box from a $d$-dimensional system to a $D$-dimensional system, we propose a universal protocol for isometry inversion that constructs a decoder from multiple calls of the encoding operation. This is a probabilistic but exact protocol whose success probability is independent of $D$. For a qubit ($d=2$) encoded in $n$ qubits, our protocol achieves an exponential improvement over any tomography-based or unitary-embedding method, which cannot avoid $D$-dependence. Isometry operations include unitary operations, but previous universal protocols for unitary inversion exploited the group structure for unitary operators. Despite isometry operators not forming a group, we present a quantum operation that converts multiple parallel calls of any given isometry operation to random parallelized unitary operations, each of dimension $d$. Applied to our setup, it universally compresses the quantum information in the encoded state to a $D$-independent space, while keeping the initial quantum information intact. This compressing operation is combined with a unitary inversion protocol to complete the isometry inversion. We also discover a fundamental difference between our isometry inversion protocol and the known unitary inversion protocols by analyzing other higher-order quantum transformation on isometry operations, namely, isometry complex conjugation and isometry transposition. General protocols including indefinite causal order are searched using semidefinite programming for any improvement in the success probability over the parallel protocols. In addition, we find a sequential ``success-or-draw'' protocol of universal isometry inversion for $d = 2$ and $D = 3$, thus whose success probability exponentially improves over parallel protocols in the number of calls of the input isometry operation for the said case.

• 14:15-15:15   (Invited) Kenta Suzuki (Kyoto U.)

  Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
  The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many-body system with random all-to-all interactions on fermionic N sites (N>>1). This model is known to saturate the maximal chaos bound of many-body system. Based on this fact, the model brought us vast amounts of insights into many-body chaos, quantum information, quantum black holes and wormholes in the sense of the AdS/CFT correspondence. In this talk, we start from reviewing basis aspects of the SYK model in the large N limit, we highlight some application of the model for many-body chaos and the so-called "near" AdS2/CFT1 correspondence. We also discuss some puzzles about wormhole geometries in the AdS/CFT and implications from the SYK model. Finally, we introduce a partially disorder-averaged SYK model, by modifying the probability distribution of the random coupling constant. We show that this model smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as the "half" of the bi-local collective fields, and we study implications of these new local collective fields for wormhole physics.



• 15:30-16:00   Zixia Wei (Kyoto U.)

  Minimally entangled typical thermal states in field theories and holography
  Minimally entangled typical thermal states (METTS) are a class of states which are mainly used for efficient numerical simulations of thermal states. In this talk, we will see that METTS arise as a natural decomposition in QFTs and show their crucial properties. Inspired by QFT, we will also show some new results of METTS from numerical simulations. We will also discuss the gravity dual of METTS, as well as its application to half-wormholes and the factorization puzzle.

• 16:00-16:30   Takato Mori (KEK)

  Entanglement entropy in interacting quantum field theories
  In this talk, we discuss the computation of half-space entanglement entropy in quantum field theories. We show that there exists a novel contribution from interaction vertices and some dominant contributions can be resummed to all orders and they can be written in terms of the two-point functions of both the fundamental and composite operators.

• 16:45-17:45   (Invited) Julian Sonner (U. Geneva)

  A universal string field theory for quantum chaos
  In this work we summarise recent as well as work to be published on a surprising and profound connection between quantum chaos and the unitarization of black-hole radiation. Quantum chaotic systems are characterised by a highly universal structure of their energy spectrum, manifested in level-correlations that follow random-matrix statistics. We will argue that this random-matrix universality has powerful implications for semiclassical gravity, and its fully non-perturbative quantum completion. In this talk we will describe an effective field theory approach to quantum chaos, based on a symmetry breaking principle we term “causal symmetry”. We then show how the salient (doubly) non-perturbative contributions are captured by this EFT. In the latter part of the talk we will describe the bulk picture of these chaotic correlations, using the example of JT gravity and its associated universe field theory. In that case the universe field theory acted on by causal symmetry is the Kodaira-Spencer theory of gravity, viewed as a closed-string field theory, whose excitations are individual JT universes.

March 23 (Wednesday)

• 9:00-10:00   (Invited) Shinsei Ryu (Princeton U.)

  Multipartite correlations in topological liquids
  I will discuss entanglement quantities in two-dimensional topologically-ordered phases that can potentially capture correlations beyond what bipartite entanglement entropy can. Specifically, I will present the calculations of the reflected entropy and entanglement negativity for topological ground states when we consider two spatial sub regions.

• 10:15-11:15   (Invited) Nick Hunter-Jones (Stanford U.)

  The long-time behavior of chaotic quantum systems: complexity growth and entropy fluctuations
  The long-time growth of quantum complexity 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 the complexity growth, saturation, and recurrence in various models, specifically focusing on random quantum circuits (a simple model of local chaotic dynamics). We’ll then discuss another long-time property of many-body systems involving increasingly rare fluctuations of subsystem entropies.

• 11:30-12:00   Ryotaro Suzuki (Freie Universität Berlin)

  Computational power of one- and two-dimensional dual-unitary quantum circuits
  Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes universal quantum computation different from classical computers. In this work, we propose a novel family of classically simulatable circuits by making use of dual-unitary quantum circuits (DUQCs), which have been recently investigated as exactly solvable models of non-equilibrium physics, and we characterize their computational power. Specifically, we investigate the computational complexity of the problem of calculating local expectation values and the sampling problem of one-dimensional DUQCs, and we generalize them to two spatial dimensions. We reveal that a local expectation value of a DUQC is classically simulatable at an early time, which is linear in a system length. In contrast, in a late time, they can perform universal quantum computation, and the problem becomes a BQP-complete problem. Moreover, classical simulation of sampling from a DUQC turns out to be hard.

• 13:30-14:00   Yosuke Mitsuhashi (U. Tokyo)

  Characterizing symmetry-protected thermal equilibrium by work extraction
  The second law of thermodynamics states that work cannot be extracted from thermal equilibrium, whose quantum formulation is known as complete passivity; A state is called completely passive if work cannot be extracted from any number of copies of the state by any unitary operations. It has been established that a quantum state is completely passive if and only if it is a Gibbs ensemble. In the present work, we investigate complete passivity protected by symmetry imposed on operations and Hamiltonians. Specifically, we prove that a quantum state is completely passive under symmetry constraints described by a connected compact Lie group, if and only if it is a generalized Gibbs ensemble (GGE) including conserved charges associated with the symmetry. Remarkably, our result applies to non-commutative symmetry such as SU(2) symmetry, suggesting an unconventional extension of the notion of GGE. Our result serves as a foundation of the resource theory of thermodynamics in the presence of symmetries, and would also lead to flexible design principles of quantum heat engines and batteries.

• 14:15-15:15   (Invited) Naoto Shiraishi (Gakushuin U.)

  Resource theories with correlated catalyst
  In resource theories, the catalyst. which is an auxiliary system not changing its own state but helping state conversion of the system, strongly enhances the power of state conversion. Recently, it has been revealed that further convertibility and clear criterion for state conversion might be obtained if we allow a small correlation between the system and the catalyst at the end of the conversion [1-4]. In this talk, we treat two resource theories, that of athermality (i.e., quantum thermodynamics) and that of asymmetry with correlated catalysts. In the first part, we prove that a state convertibility between two quantum states through a Gibbs-preserving map with a correlated catalyst is characterized by a single monotone, a free energy defined with the quantum relative entropy [5]. In other words, the second law of thermodynamics is recovered in the microscopic quantum regime if we allow a correlated catalyst. This result solves in positive a conjecture on quantum thermodynamics raised by Refs[2,6]. Our proof technique also reveals the fact that a variety of resource theories with a correlated catalyst is characterized solely by the relative entropy. In the second part, we consider marginal catalysts [1], where multiple catalysts can correlate with each other. We demonstrate that the resource theory of asymmetry with marginal catalysts is trivial, that is, all state conversion is possible through a symmetric map with marginal catalysts [7]. This result shows clear contrast to the no-broadcasting theorem that a symmetric map cannot convert a symmetric state to an asymmetric state even with a correlated catalyst [6,8]. We also show that this embezzling-like phenomena is specific to the resource theory of asymmetry, and many other resource theories do not become trivial even with marginal catalysts. If time allows, we explain a conjecture on the resource theory of asymmetry with a correlated catalyst.
  
  [1] M. Lostaglio, M. P. Muller, and M. Pastena, Phys. Rev. Lett. 115, 150402 (2015).
  [2] H. Wilming, R. Gallego, and J. Eisert, Entropy 19, 241 (2017).
  [3] M. P. Muller, Phys. Rev. X 8, 041051 (2018).
  [4] S. Rethinasamy and M. M. Wilde, Phys. Rev. Research 2, 033455 (2020).
  [5] N. Shiraishi and T. Sagawa, Phys. Rev. Lett. 126, 150502 (2021).
  [6] M. Lostaglio and M. P. Muller, Phys. Rev. Lett. 123, 020403 (2019).
  [7] Ryuji Takagi and Naoto Shiraishi, arXiv:2106.12592.
  [8] I. Marvian and R. W. Spekkens, Phys. Rev. Lett. 123, 020404 (2019).
  

• 15:30-16:00   Toshihiro Yada (U. Tokyo)

  Quantum Fluctuation Theorem under Continuous Measurement and Feedback
  The fluctuation theorem implies the thermodynamic second law and plays a central role in the field of nonequilibrium thermodynamics. While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we analytically derive the generalized fluctuation theorem under continuous quantum measurement and feedback. The essence of the derivation is to newly introduce the operationally meaningful information which we refer to as quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy is defined as the accumulation over time of the conditional QC-mutual information under the past measurement outcomes. Therefore, it can naturally be interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work elucidates the fundamental relationship between nonequilibrium thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems.



• 16:00-18:30   Poster session

March 24 (Thursday)

• 9:00-10:00   (Invited) Anurag Anshu (Harvard University)

  An area law for ground states of 2D frustration-free spin systems
  We will discuss an area law for ground states of locally gapped frustration-free 2D lattice spin systems. We first generalize the optimal approximation of the boolean AND function to a non-commuting setting, showing that the ground state projector of a locally gapped frustration-free 1D spin system can be optimally approximated in a similar manner. For 2D spin systems we then construct an approximate ground state projector (AGSP) that employs the optimal 1D approximation along the boundary of the bipartition of interest. If time permits, we will also discuss the challenges in extending the proof to 3D systems.
  Joint work with Itai Arad and David Gosset.

• 10:15-11:15   (Invited) Xiao-Liang Qi (Stanford U.)

  Quantum information measure of space-time correlation
  Most quantum information measures are defined for quantum states. For example, mutual information measures the correlation between two subsystems in a quantum state. It is natural to ask whether correlation in spacetime can be characterized by some generalization of mutual information. In this work, we propose a space-time generalization of mutual information. The key idea is to consider a general "quantum experiment" that measures the correlation between two space-time regions, and use the setup of hypothesis testing. We discuss various properties of the spacetime mutual information, including how it provides an upper bound for all connected correlation functions, which is a direct generalization of the similar property of ordinary mutual information.

• 11:30-12:00   Ryusuke Hamazaki (RIKEN))

  Exceptional dynamical quantum phase transitions in periodically driven systems
  Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a dynamical version of free energy, their nature is yet to be elusive. In this talk, we show that spontaneous symmetry breaking can occur at a short-time regime and causes universal dynamical quantum phase transitions in periodically driven unitary dynamics. Unlike conventional phase transitions, the relevant symmetry is antiunitary: its breaking is accompanied by a many-body exceptional point of a nonunitary operator obtained by space-time duality. Using a stroboscopic Ising model, we demonstrate the existence of distinct phases and unconventional singularity of dynamical free energy, whose signature can be accessed through quasilocal operators. Our results open up research for hitherto unknown phases in short-time regimes, where time serves as another pivotal parameter, with their hidden connection to nonunitary physics.

• 13:30-14:00   Hayata Yamasaki (IQOQI Vienna)

  General Quantum Resource Theories: Maximal Resources, Catalytic Replication, and Asymptotically Consistent Measures
  Quantum resource theories (QRTs) provide a unified theoretical framework for understanding inherent quantum-mechanical properties that serve as resources in quantum information processing, but resources motivated by physics may possess structure whose analysis is mathematically intractable, such as non-uniqueness of maximally resourceful states, lack of convexity, and infinite-dimensional state spaces. We investigate state conversion and resource measures in general QRTs under minimal assumptions to figure out universal properties of physically motivated quantum resources that may have such mathematical structure whose analysis is intractable. In the general setting, we prove the existence of maximally resourceful states in one-shot state conversion. Also analyzing asymptotic state conversion, we discover catalytic replication of quantum resources, where a resource state is infinitely replicable by free operations. Furthermore, we introduce consistent resource measures that quantify the amount of quantum resources without contradicting the rate of state conversion even in QRTs with non-unique maximally resourceful states. We prove that relative entropic measures are consistent with the rates for a broad class of resources, i.e., all convex finite-dimensional resources, e.g., entanglement, coherence, and magic, and even a representative class of physically motivated non-convex or infinite-dimensional resources such as quantum discord, non-Markovianity, and non-Gaussianity. Progressing beyond the previous work showing a uniqueness theorem for additive resource measures, we prove the corresponding uniqueness inequality for the consistent resource measures; that is, consistent resource measures of a quantum state take values between the distillable resource and the resource cost of the state. These formulations and results establish a foundation of QRTs applicable in a unified way to quantitative analyses of a significantly broad class of physically well-motivated inherent quantum properties.

• 14:15-15:15   (Invited) Ryuji Takagi (Nanyang Technological U.)

  Characterizing Usefulness and Limitations of Quantum Resources via Quantum Information Theory
  Quantum resources, such as quantum entanglement and superposition, are the origins of quantum phenomena observed in physical systems and are core sources of advantages in quantum information processing. In this talk, I will overview the recent developments of general resource theories, a unified framework that deals with the quantification and manipulation of a general class of quantum resources from the information-theoretic viewpoint. I will introduce general methods of quantifying the physical resources that cannot be produced by freely accessible quantum operations and show that these resource quantifiers characterize the performances of fundamental operational tasks such as channel discrimination and resource distillation. I will then describe how these general results can be applied to concrete settings such as fault-tolerant quantum computation, for which we obtain a fundamental lower bound of the overhead incurred on an arbitrary magic-state distillation and gate synthesis protocol, and quantum communication, for which we derive quantum capacity and simulation cost for several communication settings in a single unified manner. Potential applications to quantum thermodynamics and many-body physics will also be discussed.

• 15:30-16:00   Atsushi Iwaki (U. Tokyo)

  Purity of thermal mixed quantum states
  It is known that the microscopically different states at finite temperature in thermal equilibrium can be microscopically different in their descriptions. The two limiting cases are the Gibbs state which is the exponentially large numbers of mixtures of pure states with zero purity, and the thermal pure quantum (TPQ) state which is a single quantum state with purity-1. Here, we propose a series of thermal mixed quantum (TMQ) states that have purity in between 0 and 1, which can be generated by random sampling methods. We regard all of them as describing the same thermal equilibrium in the sense that they are indistinguishable if we focus on the local observables or the density matrix of a relatively large but small enough subsystem. There are several ways to construct a series of TMQ states, e.g. those using the matrix product representation, starting from the randomly sampled state and performing an imaginary time evolution. The degree of how many states need to be mixed, which may roughly be given as the number of samples to take, depends much on the methods, which are larger for smaller purity. However, unfortunately, the way to measure the purity was lacking. Here, we develop an analytical formulation to describe the purity of the TMQ state using the measurable quantity, normalized fluctuation of the partition function. We apply this formula to the RPMPS+T and TPQ-MPS methods and show that the purity could be measured and could explain the features of these methods.

• 16:00-16:30   Masaru Hongo (U. Illinois Chicago)

  Hydrodynamics from local thermal pure quantum states
  We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum (lTPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the ℓTPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic relaxation obeying the Fourier's law. We further prove the second law of thermodynamics and the quantum fluctuation theorem, which are also validated numerically. The lTPQ formulation gives a useful theoretical basis to describe the emergent hydrodynamic behavior of quantum many-body systems furnished with a numerical efficiency, being applicable to both the non-relativistic and relativistic regimes.

March 25 (Friday)

• 9:00-10:00   (Invited) Marcos Rigol (Pennsylvania State U.)

  Typical eigenstate entanglement entropy as a diagnostic of quantum chaos and integrability The typical entanglement entropy of subsystems of random pure states is known to be (nearly) maximal, while the typical entanglement entropy of random Gaussian pure states has been recently shown to exhibit a qualitatively different behavior, with a coefficient of the volume law that depends on the fraction of the system that is traced out. In this talk, we summarize old as well as recent rigorous results for those starkly different classes of states [1]. We then show that the typical entanglement entropy of eigenstates of a local quantum-chaotic Hamiltonian mirrors the former behavior [2], while that of a local integrable Hamiltonian mirrors the latter [3]. Based on these results, we conjecture that the typical entanglement entropy of Hamiltonian eigenstates can be used as a diagnostic of quantum chaos and integrability [3]. We discuss subtleties that emerge as a result of conservation laws, such as particle number conservation [1,2], as well as of lattice translational invariance [4].
  
  [1] E. Bianchi, L. Hackl, M. Kieburg, MR, and L. Vidmar, arXiv:2112.06959.
  [2] L. Vidmar and MR, PRL 119 220603 (2017).
  [3] T. LeBlond, K. Mallayya, L. Vidmar, and MR, PRE 100 062134 (2019).
  [4] L. Vidmar, L. Hackl, E. Bianchi, and MR, PRL 119 020601 (2017).
  

• 10:15-10:45   Ryosuke Yoshii (Sanyo Onoda City U.))

  Entanglement propagation in thermalization of an isolated quantum system
  We study dynamics of entanglement in the thermalization process of an isolated quantum many-body system. We propose a simple setup for measuring the propagation speed of entanglement entropy (EE) in numerical simulations and apply it to the integrable/non-integrable spin models in 1D - the transverse Ising (TI) model, the chaotic Ising (CI) model, and the extended chaotic Ising (ECI) model. We find that two distinct time-scales t* and tdiff arise in the dynamics of EE in the thermalization process: the former represents the time-scale for the saturation of EE and the latter characterizes spreading of EE over the entire system. Evaluating the propagation speed of entanglement from tdiff, we find that entanglement propagates ballistically with a constant velocity irrespective of the integrability of the model. The propagation speed of entanglement is found to coincide with the maximum group velocity of quasi-particle excitations in the TI model. We also evaluate the propagation speed of entanglement by mutual information and find the characteristic time-scale tMI. We show that the propagation speeds of entanglement evaluated by tMI and tdiff agree well. We discuss the condition for thermalization based on the numerical results and propose that scrambling of the entire system has to take place before saturation of EE for thermalization.

• 10:45-11:15   Gen Kimura (Shibaura Institute of Technology)

  Universal Constraints on relaxation rates for open quantum Markovian dynamics
  We establish a universal constraint on relaxation rates which is valid for a general quantum Markovian dynamics with d-level. The constraint serves as an experimental verification for the completely positive condition which is widely accepted in the field of open quantum system as well as quantum information community. We also discuss several operator-norm inequalities from a technical point of view of our study.

• 11:15-11:45   Yasuhiro Tada (Hiroshima U.)

  Lieb-Schultz-Mattis theorem in long-range interacting systems
  Lieb-Schultz-Mattis (LSM) theorem is a fundamental theorem in quantum many-body systems. It can exclude simple short-range entangled states based only on particle-fillings, and therefore can be a good starting point for studying long-range entangled states. In this study, we extend LSM theorem to long-range interacting systems including realistic Coulomb interactions.

• 11:45-11:50   Closing remarks