Research Fellow
National University of Singapore, Centre for Quantum Technologies.
Research
I am currently a Research Fellow at Centre for Quantum Technologies, National University of Singapore.
My researh focused on the quantum information theory, quantum computation theory and topologial order.
Physics and Mathematicas
- Topological order, TQFT, Chern-Simons theory
- CFT, RCFT
- Quantum information, quantum computation
- SPT, SET
- IT FROM QUBIT
- AdS/CFT, AdS/CMT
- Tensor cateogory, Frobenius algebra
- Vertex operator algebra
- Functional analysis, operator algebra, convex analysis, finite geometry
- Group cohomology, higher category
Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.
Curriculum Vitae
Please click here for a full pdf version of my CV (updated intermittently)
Intro
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Zhian JiaThe world is our oyster
I am passionate about all things interesting, including but not limited to physics, mathematics, poetry, music, literature, etc.
Academic Experience
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present 2021
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2019 2018
Visiting Scholar
University of California, Santa Barbara, Department of Mathematics and Station Q.
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2018 2017
Visiting PhD
Tsinghua University, Yau Mathematical Sciences Center
Education
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Ph.D. 2021
Ph.D. in Physics
University of Science and Technology of China, CAS Key Laboratory of Quantum Information.
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B.S.2015
Physics
Central South University, Department of physics.
“Life's but a walking shadow; a poor player, that struts and frets his hour upon the stage, and then is heard no more: it is a tale told by an idiot, full of sound and fury, signifying nothing.”
Contribution to the Mathematical and Physical Community
- AMS Mathematical Reviews
- Journal of High Energy Physics (JHEP)
- Quantum
- SciPost Physics
- Journal of Physics A: Mathematical and Theoretical
- Journal of Physics B: Atomic, Molecular and Optical Physics
- Advanced Quantum Technologies
- Physica Scripta
- Journal of Knot Theory and Its Ramifications
- International Journal of Quantum Information
- Intelligent Computing
Attended conferences and workshops
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April 1 - 4, 2024
Beijing Institute of Mathematical Sciences and Applications (BIMSA), quantum symmetry seminar
Talk: Hopf symmetries behind 2d topological phases [,]
Beijing, China -
Jan 2 - 5, 2024
The 2023 Annual International Congress of Chinese Mathematicians (ICCM2023)
Fudan University, Shanghai, China
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Dec 11 - 15, 2023
Quantum Resources 2023
Nanyang Technological University, Singapore
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Nov 20 - 24, 2023
Quantum Energy Initiative Workshop 2023
National University of Singapore, Singapore
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Sep 27 - 29, 2023
IPS Meeting 2023
National University of Singapore, Singapore
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Sep 18 - 23, 2023
YIPQS long-term workshop: Quantum Information, Quantum Matter and Quantum Gravity
Talk: Gapped boundary theory of Hopf and weak Hopf quantum double model [ , ]
Yukawa Institute for Theoretical Physics, Kyoto University, Japan -
Nov 5 - 8, 2022
Quantum resources: from mathematical foundations to operational characterisation
Nanyang Technological University, Singapore
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Sept 28 - 30, 2022
IPS Meeting 2022
SPMS, Nanyang Technological University, Singapore
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Aug 1 - 5, 2022
CQT Scientific Advisory Board Meeting
CQT, National University of Singapore, Singapore
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Oct 14-15, 2021
Quantum Boundaries 2021 (Online)
University of Nottingham, Nottingham
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Nov 23 - 25, 2020
Fields, Gravity and Information (Online)
Fudan University, Shanghai, China
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Dec 16 - 20, 2019
Topological quantum computing (TQC2019)
Southern University of Science and Technology, Peng Cheng Laboratory Institute for quantum science and engineering, Shenzhen, China
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Aug 13 - 17, 2018
Summer school on AdS/CFT
Center for High Energy Physics, Peking University, Beijing, China
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Jul 16 - 20, 2018
Tsinghua Summer School on Quantum Physics (TSSQP)
State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing, China
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Jul 4-6,2018
The First International Conference on Machine Learning and Physics
Institute for Advanced Study, Tsinghua University, Beijing, China
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May 4-6,2018
Conference: Topological Matter and Topological Computation
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, China
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Mar 19 - 23, 2018
Quantum Machine Learning and Biomimetic Quantum Technologies
University of the Basque Country, Leioa, Spain
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Jun 20 - 30, 2017
Workshop: Tensor categories and topological quantum matter
Fudan University, Shanghai, China
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Jun 4 - 5, 2017
Workshop: Quantum Contextuality in Quantum Mechanics and Beyond
Prague, Czech Republic
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Jan 23 - 26, 2017
Conference on 90 Years of Quantum Mechanics
Nanyang technological university, Singapore
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Jun 16- Jul 16, 2016
Summer School on Supersymmetry and Fiber bundle
University of Chinese Academy of Sciences, Beijing, China
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Aug 6-8,2016
The 17th National Conference on Quantum Optics
Lanzhou university, Lanzhou, China
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May 23 - 24, 2015
The First Conference of The Second Revolution of Quantum Mechanics
University of Science and Technology of China, Hefei, China
Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.
Research Interests
My research focused quantum information and quantum computation, topological order and TQFT, quantum topology and algebra, etc.
TQFT, CFT, tensor category, Hopf algebra.
Topological order, SPT, SET.
Topological quantum error-correcting code, homological code, topological quantum computation.
Space-time states, pseudo-density operator, superdensity operator.
Quantum causality, process matrix.
Quantum correlations: quantum discod, quantum entanglement, quantum steering, Bell nonlocality.
Quantum contextuality.
Research Interests
- Mathematical physics
- Topological Order & TQFT
- Quantum field theory
- Quantum topology & algebra
- Tensor category
- Quantum Information theory
- Quantum Foundations
- Quantum Computation theory
- Condensed matter
- Hopf algebra
- Tensor Network & Neural Network
- Quantum Machine Learning
Current Research Projects
A list of my current research directions.
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Coming soon...
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Coming soon...
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Coming soon...
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Coming soon...
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Coming soon...
Research is what I'm doing when I don't know what I'm doing.
Publications and preprints
Many of my preprints/publications are now accessible on arXiv. A more comprehensive list is on my google scholar page.
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Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
[arXiv:2405.09277] | 2024
Abstract
Cluster states are crucial resources for measurement-based quantum computation (MBQC). It exhibits symmetry-protected topological (SPT) order, thus also playing a crucial role in studying topological phases. We present the construction of cluster states based on Hopf algebras. By generalizing the finite group valued qudit to a Hopf algebra valued qudit and introducing the generalized Pauli-X operator based on the regular action of the Hopf algebra, as well as the generalized Pauli-Z operator based on the irreducible representation action on the Hopf algebra, we develop a comprehensive theory of Hopf qudits. We demonstrate that non-invertible symmetry naturally emerges for Hopf qudits. Subsequently, for a bipartite graph termed the cluster graph, we assign the identity state and trivial representation state to even and odd vertices, respectively. Introducing the edge entangler as controlled regular action, we provide a general construction of Hopf cluster states. To ensure the commutativity of the edge entangler, we propose a method to construct a cluster lattice for any triangulable manifold. We use the 1d cluster state as an example to illustrate our construction. As this serves as a promising candidate for SPT phases, we construct the gapped Hamiltonian for this scenario and delve into a detailed discussion of its non-invertible symmetries. We also show that the 1d cluster state model is equivalent to the quasi-1d Hopf quantum double model. We also introduce the Hopf tensor network representation of Hopf cluster states by integrating the tensor representation of structure constants with the string diagrams of the Hopf algebra.
Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model
[arXiv:2403.04446] | 2024
Abstract
We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra, leading to a reducible vacuum string label; the charge symmetry, serving as a quantum double of gauge symmetry, constitutes a connected weak Hopf algebra. This implies that the associated topological phase retains its characterization by a unitary modular tensor category (UMTC). The bulk charge symmetry can also be captured by a weak Hopf tube algebra. We offer an explicit construction of the weak Hopf tube algebra structure and thoroughly discuss its properties. The gapped boundary and domain wall models are extensively discussed, with these 1d phases characterized by unitary multifusion categories (UMFCs). We delve into the gauge and charge symmetries of these 1d phases, as well as the construction of the boundary and domain wall tube algebras. Additionally, we illustrate that the domain wall tube algebra can be regarded as a cross product of two boundary tube algebras. We establish the anyon condensation theory to elucidate the bulk-to-boundary and bulk-to-wall condensation phenomena from UMTCs to a UMFCs. As an application of our model, we elucidate how to interpret the defective string-net as a restricted multifusion string-net.
Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states
Abstract
We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have shown that bipartite two-time states can reproduce the statistics of bipartite process matrices. Here, we show that the operational scenarios underlying two-time states can be represented as PDMs, and thereby construct a mapping from process matrices to PDMs. The existence of this mapping implies that PDMs can, like the process matrix, model processes with indefinite causal orders. We illustrate this ability by showing how negativity of the PDM, a measure of temporal correlations, is activated by creating a quantum-switched order of operators associated with reset channels. The results contribute to the unification of quantum models of spatiotemporal states.
The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
preprint
[arXiv:2305.15649] | 2023
[arXiv:2305.15649] | 2023
Abstract
The measurement statistics for spatial and temporal quantum processes are produced through distinct mechanisms. Measurements that are space-like separated exhibit non-signaling behavior. However, time-like separated measurements can only result in one-way non-signaling, as the past is independent of the future, but the opposite is not true. This work presents the doubled density operator as a comprehensive framework for studying quantum processes in space-time. It effectively captures all the physical information of the process, with the measurement and Born rule showing uniformity for both spatial and temporal cases. We demonstrate that the equal-time density operator can be derived by performing a partial trace operation on the doubled density operator. Furthermore, the temporality of the quantum process can be detected by conducting a partial trace operation on either the left or right half of the doubled density operator.
Quantum space-time marginal problem: global causal structure from local causal information
Abstract
Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators, and quantum causality between the involved events in an experiment is encoded in the corresponding pseudo-density operator. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the pseudo-density operators; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle, which can be solved effectively by using a neural network. The notion of quantum pseudo-channel is also introduced and we demonstrate that the quantum pseudo-channel marginal problem can be solved by transforming it into a pseudo-density operator marginal problem via the channel-state duality.
On weak Hopf symmetry and weak Hopf quantum double model
Abstract
Symmetry is a central concept for classical and quantum field theory, usually, symmetry is described by a finite group or Lie group. In this work, we introduce the weak Hopf algebra extension of symmetry, which arises naturally in anyonic quantum systems; and we establish weak Hopf symmetry breaking theory based on the fusion closed set of anyons. As a concrete example, we implement a thorough investigation of the quantum double model based on a given weak Hopf algebra and show that the vacuum sector of the model has weak Hopf symmetry. The topological excitations and ribbon operators are discussed in detail. The gapped boundary and domain wall theories are also established, we show that the gapped boundary is algebraically determined by a comodule algebra, or equivalently, a module algebra; and the gapped domain wall is determined by the bicomodule algebra, or equivalently, a bimodule algebra. The microscopic lattice constructions of the gapped boundary and domain wall are discussed in detail. We also introduce the weak Hopf tensor network states, via which we solve the weak Hopf quantum double lattice models on closed and open surfaces. The duality of the quantum double phases is discussed in the last part.
Boundary and domain wall theories of 2d generalized quantum double model
Abstract
The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of topological excitations based on the representations of the quantum double of Hopf algebras are discussed. To generalize the model to a 2d surface with boundary and surface defect, we present a systematical construction of the boundary Hamiltonian and domain wall Hamiltonian using Hopf algebra pairing and generalized quantum double construction. Via the Hopf tensor network representation of the quantum many-body states, we solve the ground state of the model in the presence of the boundary and domain wall.
Antilinear superoperator and quantum geometric invariance for higher-dimensional quantum systems
preprint
[arXiv:2202.10989] | 2022
[arXiv:2202.10989] | 2022
Abstract
We present an investigation of the antilinear superoperators and their applications in studying higher-dimensional quantum systems. The antilinear superoperators are introduced and various properties are discussed. We study several crucial classes of antilinear superoperators, including antilinear quantum channels, antilinearly unital superoperators, antiunitary superoperators and the generalized theta-conjugation. Then using the Bloch representation, we present a systematic investigation of the quantum geometric transformations of higher-dimensional quantum systems. By choosing different generalized Θ-conjugation, different metrics for the space of Bloch space-time vectors are obtained, including the Euclidean metric and Minkowskian metric. Then using these geometric structures, we investigate the entanglement distribution over a multipartite system restricted by quantum geometric invariance.
Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory
preprint
[arXiv:2201.12361] | 2022
[arXiv:2201.12361] | 2022
Abstract
Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT), its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the symmetry enriched generalization of the model for the cyclic Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the symmetry enriched topological (SET) phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the -crossed unitary braided fusion category (UBFC). By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. Then we carefully construct the explicit lattice realization of EM duality for these SET phases. Finally, their potential applications in topological quantum computation and topological memory theories are discussed.
Quantum simulation of indefinite causal order induced quantum refrigeration
Abstract
In the classical world, physical events always happen in a fixed causal order. However, it was recently revealed that quantum mechanics allows events to occur with indefinite causal order (ICO). In this study, we use an optical quantum switch to experimentally investigate the application of ICO in thermodynamic tasks. Specifically, we simulate the working system interacting with two identical thermal reservoirs in an ICO, observing the quantum heat extraction even though they are in thermal equilibrium where heat extraction is unaccessible by traditional thermal contact. Using such a process, we simulate an ICO refrigeration cycle and investigate its properties. We also show that by passing through the ICO channel multiple times, one can extract more heat per cycle and thus obtain a higher refrigeration performance. Our results suggest that the causal nonseparability can be a powerful resource for quantum thermodynamic tasks.
Quantum advantages of communication complexity from Bell nonlocality
Abstract
Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, for which several distributed parties attempt to jointly calculate a given function with limited classical communications. In this work, we present a method to construct CC problems from Bell tests in a graph-theoretic way. Starting from an experimental compatibility graph and the corresponding Bell test function, a target function that encodes the information of each edge can be constructed; then, using this target function, we can construct a CC function, and by pre-sharing entangled states, its success probability exceeds that of the arbitrary classical strategy. The non-signaling protocol based on the Popescu–Rohrlich box is also discussed, and the success probability in this case reaches one.
Environment-induced sudden change of coherence in quantum systems
Abstract
Manipulating dynamical evolution is an important task in quantum information. The sudden death phenomenon (SDP), which is predicted to be unattainable beyond entanglement [T. Yu and J. H. Eberly, Sudden death of entanglement, Science 323, 598 (2009)], would be an especially surprising feature in quantum coherence. In this paper, we modulate the spatial modes of photons and build a spatially inclined channel using a series of specially made quartz plate pairs. Within this channel, sudden changes in coherence occur in open-quantum systems. We, then, describe the SDP within a general theoretical framework of sudden quantum-coherence changes and by defining the nth order sudden coherence change. Moreover, by adding non-Markovian noise, we find that coherence can rebirth after a sudden death. We further compare the sudden change features in coherence and quantum entanglement. We find that both coherence and entanglement perform identical dynamical processes upon Bell diagonal states, although their dynamical characteristics change when the initial state is partially entangled. Our results provide insights into the sudden change phenomena of quantum correlations beyond entanglement along with intriguing perspectives on quantum coherence dynamics.
Entanglement area law for shallow and deep quantum neural network states
Abstract
A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.
Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists
Abstract
Machine learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We explore one of the most important representations, restricted Boltzmann machine (RBM) representation, in stabilizer formalism. We give the general method of constructing RBM representation for stabilizer code states and find the exact RBM representation for several types of stabilizer groups with the number of hidden neurons equal or less than the number of visible neurons, which indicates that the representation is extremely efficient. Then we analyze the surface code with boundaries, defects, domain walls and twists in full detail and find that all the models can be efficiently represented via RBM ansatz states. Besides, the case for Kitaev's $D(\Zb_d)$ model, which is a generalized model of surface code, is also investigated.
Quantum neural network states: a brief review of methods and applications
Abstract
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schrödinger equations of the system. But typically, many physical systems have a simplified internal structure which makes the parameters needed to characterize their ground states exponentially smaller. This makes many numerical methods possible in capture the physics of the system. Among these modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of the big data, are now attracting many interests. Neural network representation of quantum many-body states shows great potential in solving some traditionally difficult quantum problems involving large number of freedoms. In this work, we briefly review the progress of using the artificial neural network to build quantum many-body ansatz states. We take Boltzmann machine representation as a prototypical example to illustrate various aspects of neural network representation of quantum many-body states. We first briefly review the classical neural networks, then we illustrate how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states, including entanglement features, representational power, and the relation with tensor network states, are discussed. For applications, we briefly review the progress of many-body calculating based on neural network states, neural network state approach to tomography, and also the classical simulation of quantum computing based on Boltzmann machine states. At the end of the work, some outlooks and open problems are given.
Experimentally detecting a quantum change point via Bayesian inference
Abstract
Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this work, we consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.
An efficient algorithmic way to construct Boltzmann machine representations for arbitrary stabilizer code
Abstract
The restricted Boltzmann machine (RBM) has seen great success as a variational quantum state, but its representational power is far less understood. We analytically give the first proof that RBMs can exactly and efficiently represent stabilizer code states, a family of highly entangled states of great importance in the field of quantum error correction. Given the stabilizer generators, we present an efficient algorithm to compute the structure of the RBM, as well as the exact values of RBM parameters. This opens up a new perspective on the representational power of RBMs, justifying the success of RBMs in representing highly entangled states, and is potentially useful in the classical simulation of quantum error-correcting codes.
Entropic no-disturbance as a physical principle
Abstract
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entropic contextuality and entropic nonlocality are investigated in depth in this framework. We show how one can construct monogamy relations using entropic cone and basic Shannon-type inequalities. The general criterion for several entropic tests to be monogamous is also developed, using the criterion, we demonstrate that entropic nonlocal correlations are monogamous, entropic contextuality tests are monogamous and entropic nonlocality and entropic contextuality are also monogamous. Finally, we analyze the entropic monogamy relations for multiparty and many-test case, which plays a crucial role in quantum network communication.
Hierarchy of genuine multipartite quantum correlations
Abstract
Classifying states which exhibiting different statistical correlations is among the most important problems in quantum information science and quantum many-body physics. In bipartite case, there is a clear hierarchy of states with different correlations: total correlation (T) ⊋ discord (D) ⊋ entanglement (E) ⊋ steering (S) ⊋ Bell~nonlocality (NL). However, very little is known about genuine multipartite correlations (GM) for both conceptual and technical difficulties. In this work, we show that, for any N-partite qudit states, there also exist such a hierarchy: genuine multipartite total correlations (GMT) ⊇ genuine multipartite discord (GMD) ⊇ genuine multipartite entanglement (GME) ⊇ genuine multipartite steering (GMS) ⊇ genuine multipartite nonlocality (GMNL). Furthermore, by constructing precise states, we show that GMT, GME and GMS are inequivalent with each other, thus GMT ⊋ GME ⊋ GMS.
Geometric local-hidden-state model for some two-qubit states
Abstract
Adopting the geometric description of steering assemblages and the local-hidden-state (LHS) model, we construct the optimal LHS model for some two-qubit states under continuous projective measurements and obtain a sufficient steering criterion for all two-qubit states. Using the criterion, we show more two-qubit states that are asymmetric in the steering scenario under projective measurements. Then we generalize the geometric description into higher-dimensional bipartite cases, calculate the steering bound of two-qutrit isotropic states, and discuss more general cases.
Geometric steering criterion for two-qubit states
Abstract
According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A quantity is introduced to describe the required local resources to reconstruct a measurement assemblage for two-qubit states. We show that the quantity can be regarded as a quantification of steerability and be used to find out optimal LHS models. Finally we propose a method to generate unsteerable states, and construct some two-qubit states which are entangled but unsteerable under all projective measurements.
Characterizing Nonlocal Correlations via Universal Uncertainty Relations
Abstract
Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. In the course of our study, the uncertainty relations are formulated in majorization form, and the uncertainty quantifier can be chosen as any convex Schur concave functions, this leads to a large set of inequalities, including all existing criteria based on entropies. We address the question that if all steerable states (or entangled states) can be witnessed by some uncertainty-based inequality, we find that for pure states and many important families of states, this is the case.
Abstract
Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognised as a consequence of exclusivity principle(EP). We provide an operational criterion for monogamy: if the fractional packing number of the graph corresponding to the union of event sets of several physical experiments does not exceed the sum of independence numbers of each individual experiment graph, then these experiments are monogamous. As applications of this observation, several examples are provided, including the monogamy for experiments of Clauser-Horne-Shimony-Holt (CHSH) type, Klyachko-Can-Binicioğlu-Shumovsky (KCBS) type, and for the first time we give some monogamy relations of Swetlichny's genuine nonlocality. We also give the necessary and sufficient condition for several experiments to be monogamous: several experiments are monogamous if and only if the Lovász number the union exclusive graph is less than or equal to the sum of independence numbers of each exclusive graph.
Monogamy relation in no-disturbance theories
Abstract
The monogamy is a fundamental property of Bell nonlocality and contextuality. In this article, we studied the n-cycle noncontextual inequalities and generalized CHSH inequalities in detail and found the sufficient conditions for those inequalities to be hold. According to those conditions, we provide several kind of tradeoff relations: monogamy of generalized Bell inequalities in non-signaling framework, monogamy of cycle type noncontextual inequalities and monogamy between Bell inequality and noncontextual inequality in general no-disturbance framework. At last, some generic tradeoff relations of generalized CHSH inequalities for n-party physical systems, which are beyond one-to-many scenario, are discussed.
First-Principles Calculations of Electronic Properties of Defective Armchair MoS2 Nanoribbons
Abstract
We investigated the electronic properties of armchair MoS2 nanoribbons with vacancy defects using a first-principles method based on density functional theory. It was found that defects reduced the stability of armchair MoS2 nanoribbons. Mo vacancies and MoS2 triple vacancies can both change the band structures of nanoribbons from semiconductor to metallic, whereas S vacancies, 2S divacancies, and MoS divacancies only decrease the bandgap. The densities of states and eigenstates of the nanoribbons indicated that impurity bands near the Fermi level basically contributed to the defect states. The relationships between the bandgap and width of four types of semiconducting nanoribbons were simulated. Nanoribbons with no defects have a bandgap that oscillates with width in a period of three, but the bandgap changes nonperiodically for nanoribbons with S vacancies, 2S divacancies, and MoS divacancies. We also found that when the concentration of defects decreased, the vacancy defects did not destroy the nanoribbon semiconducting behavior but only decreased the bandgap. These results open up possibilities for MoS2 nanoribbon applications in novel nanoelectronic devices.
Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.
Seminars
The page is for seminars, talks and other academic stuffs.
Currrent Seminars
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2022 July2022 June
Former Seminars
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2016-2021
QI, QC, TO, TQFT
etc.