arXiv subjects

Xiao-Liang Qi

Publications and source records attributed to Xiao-Liang Qi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Measurement-Induced Entanglement Phase Transition in Random Bilocal Circuits

Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper, we study the dynamics of averaged purity for a simple $N$-qudit Brownian circuit model with all-to-all random interaction and measurements. In the large-$N$ limit, our model is mapped to a one-dimensional quantum chain in the semi-classical limit, which allows us to analytically study critical behaviors and various other properties of the model. We show that there are two phases distinguished by the behavior of the total system entropy in the long time. In addition, the two phases also have distinct subsystem entropy behavior. The low measurement rate phase has a first-derivative discontinuity in the behavior of second Renyi entropy versus subsystem size, similar to the "Page curve" of a random state, while the other phase has a smooth entropy curve.

quant-ph↗

arXiv2021

Holevo Information and Ensemble Theory of Gravity

Holevo information is an upper bound for the accessible classical information of an ensemble of quantum states. In this work, we use Holevo information to investigate the ensemble theory interpretation of quantum gravity. We study the Holevo information in random tensor network states, where the random parameters are the random tensors at each vertex. Based on the results in random tensor network models, we propose a conjecture on the holographic bulk formula of the Holevo information in the gravity case. As concrete examples of holographic systems, we compute the Holevo information in the ensemble of thermal states and thermo-field double states in the Sachdev-Ye-Kitaev model. The results are consistent with our conjecture.

hep-th↗

arXiv2021

Emergent classicality in general multipartite states and channels

In a quantum measurement process, classical information about the measured system spreads throughout the environment. Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an $O(1)$-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of arXiv:1310.8640 in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the "quantum Markov blanket" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.

quant-ph↗

arXiv2021

Quantum Algorithmic Measurement

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms and interactive protocols. We use the QUALM framework to study two important experimental problems in quantum many-body physics: determining whether a system's Hamiltonian is time-independent or time-dependent, and determining the symmetry class of the dynamics of the system. We study abstractions of these problem and show for both cases that if the experimentalist can use her experimental samples coherently (in both space and time), a provable exponential speedup is achieved compared to the standard situation in which each experimental sample is accessed separately. Our work suggests that quantum computers can provide a new type of exponential advantage: exponential savings in resources in quantum experiments.

quant-ph↗

arXiv2021

Holographic entanglement negativity and replica symmetry breaking

Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.

hep-th↗

arXiv2020

Rescuing a black hole in the large-$q$ coupled SYK model

In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-$q$ theory with the bulk low energy effective theory. In particular, we study the special case of a ``rescued black hole'', which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS$_2$ vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-$q$ and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

hep-th↗

arXiv2020

Size of bulk fermions in the SYK model

The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS$_2$ bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk $\text{SL}(2; \mathbb{R})$ generators.

hep-th↗

arXiv2020

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition

We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.

quant-ph↗

arXiv2020

Effective entropy of quantum fields coupled with gravity

Entanglement entropy quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a gravitational path integral on replica geometry with a co-dimension-$2$ brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. By introducing ancilla systems, we show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

hep-th↗

arXiv2020

Building Bulk Geometry from the Tensor Radon Transform

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of $\mathrm{AdS}_3/\mathrm{CFT}_2$. We find that, given the boundary entanglement entropies of a $2$d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

hep-th↗

arXiv2020

Replica wormhole and information retrieval in the SYK model coupled to Majorana chains

Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Rényi entropy of the Sachdev-Ye-Kitaev (SYK) model ($χ$) coupled to a Majorana chain bath ($ψ$). The system is prepared in the thermofield double (TFD) state and then evolved by $H_L+H_R$. For small system-bath coupling, we find that the second Rényi entropy $S^{(2)}_{χ_L, χ_R}$ of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a "replica wormhole". The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.

hep-th↗

arXiv2020

A Random Unitary Circuit Model for Black Hole Evaporation

Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is driven by the continuous limit of certain $2$-local random unitary circuits. We study both cases where the unitaries are chosen with and without a conserved $U(1)$ charge and focus on two aspects of the dynamics. First, we study analytically and numerically the growth of the entanglement entropy of the system, showing that two different time scales appear: one is intrinsic to the internal dynamics (the scrambling time), while the other depends on the system-environment coupling. In the presence of a $U(1)$ conserved charge, we show that the entanglement follows a Page-like behavior in time: it begins to decrease in the middle stage of the "evaporation", and decreases monotonically afterwards. Second, we study the time needed to retrieve information initially injected in the system from measurements on the environment qudits. Based on explicit numerical computations, we characterize such time both when the retriever has control over the initial configuration or not, showing that different scales appear in the two cases.

hep-th↗

arXiv2020

The Coupled SYK model at Finite Temperature

Sachdev-Ye-Kitaev (SYK) model, which describes $N$ randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS$_2$ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS$_2$ geometry. This geometry is an "eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the $q$ dependence of the spectral function.

hep-th↗

arXiv2019

Quantum Causal Influence

We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the causal relationships between putative spacetime subsystems. Our analysis reveals a quantum generalization of the thermodynamic arrow of time and begins to explore the roles of entanglement, scrambling and quantum error correction in the emergence of spacetime. For instance, exotic causal relationships can arise due to dynamically induced quantum error correction in spacetime: there can exist a spatial region in the past which does not causally influence any small spatial regions in the future, but yet it causally influences the union of several small spatial regions in the future. We provide examples of quantum causal influence in Hamiltonian evolution, quantum error correction codes, quantum teleportation, holographic tensor networks, the final state projection model of black holes, and many other systems. We find that the quantum causal influence provides a unifying perspective on spacetime correlations in these seemingly distinct settings. In addition, we prove a variety of general structural results and discuss the relation of quantum causal influence to spacetime quantum entropies.

hep-th↗

arXiv2019

Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK

In many-body chaotic systems, the size of an operator generically grows in Heisenberg evolution, which can be measured by certain out-of-time-ordered four-point functions. However, these only provide a coarse probe of the full underlying operator growth structure. In this article we develop a methodology to derive the full growth structure of fermionic systems, that also naturally introduces the effect of finite temperature. We then apply our methodology to the SYK model, which features all-to-all $q$-body interactions. We derive the full operator growth structure in the large $q$ limit at all temperatures. We see that its temperature dependence has a remarkably simple form consistent with the slowing down of scrambling as temperature is decreased. Furthermore, our finite-temperature scrambling results can be modeled by a modified epidemic model, where the thermal state serves as a vaccinated population, thereby slowing the overall rate of infection.

hep-th↗

arXiv2019

Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information

We consider the Brownian SYK model of $N$ interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-$2$ tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of $N$ qudits, where the Hamiltonian displays site-permutational symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with $N$, allowing us to perform numerically exact calculations up to $N = 10^6$. We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time $t^\ast\sim \ln N$ controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values.

quant-ph↗

arXiv2019

Integrable and chaotic dynamics of spins coupled to an optical cavity

We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop `dressing tails' of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-$S$ limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in light of the limitations set by cavity dissipation.

cond-mat.stat-mech↗

arXiv2019

Majorana fermions and the Sensitivity Conjecture

Recently, Hao Huang proved the Sensitivity Conjecture, an important result about complexity measures of Boolean functions. We will discuss how this simple and elegant proof turns out to be closely related to physics concepts of the Jordan-Wigner transformation and Majorana fermions. This note is not intended to contain original results. Instead, it is a translation of the math literature in a language that is more familiar to physicists, which helps our understanding and hopefully may inspire future works along this direction.

cond-mat.stat-mech↗