arXiv subjects

Youning Li

Publications and source records attributed to Youning Li.

12 recordsLinked to original sources

arXiv2026

Geometric-Symmetry Logical Gate and Local-Probe Selectivity in the Three-Leg AKLT Ladder

Symmetry-protected topological (SPT) phases provide a platform for encoding quantum information in protected boundary degrees of freedom. Here we study the three-leg Affleck-Kennedy-Lieb-Tasaki (AKLT) ladder as an exactly solvable SPT system with on-site symmetry $SO(3)\times \mathbb{Z}_2$. Using an exact matrix product state construction, we characterize the symmetry action on the edge encoding space and the accessibility of this space by local operators. We find that the continuous $SO(3)$ symmetry induces boundary rotations, while the leg-exchange symmetry generates a geometry-dependent logical permutation of edge qubits. Furthermore, by introducing a distinguishability measure motivated by the Knill--Laflamme condition, we derive a symmetry-resolved decay law for local accessibility. The decay is controlled by a selection rule raised from the Wigner--Eckart theorem, whereby a rank-$\ell$ local operator couples only to the $\mathcal L=\ell$ transfer-matrix sector, with a decay length determined by the corresponding correlation length. We further identify a finite-size channel that is independent of the probe operator position. These results establish a quantitative connection between SPT symmetry, lattice geometry, and the protection of boundary-encoded quantum information.

quant-ph↗

arXiv2025

Understanding the Optical Theorem of Scattering: Scattering Surface Area against Scattering Cross Section, an Example with Ellipsoidal Scattering

In this paper, we propose using the scattering surface area rather than the scattering cross section to characterize the scattering behavior of ellipsoidal rigid bodies. We examined the scattering behavior of ellipsoidal rigid bodies, focusing on the relationship between their surface area and total scattering cross-section. Building on the foundational work of Carson Flammer, we utilize the spheroidal coordinate system to derive solutions for both prolate and oblate spheroids. Our analysis reveals that under the long-wavelength approximation, the total scattering cross-section is equivalent to the surface area of the ellipsoid, a relationship that holds true for both small and moderate eccentricities. This finding extends the established optical theorem, previously validated for spherical bodies, to more complex geometries.

physics.optics↗

arXiv2024

Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields

This work presented a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterized parameter regimes and evolution time windows where the decomposition achieved measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model.

quant-ph↗

arXiv2023

Tapping into Permutation Symmetry for Improved Detection of k-Symmetric Extensions

Symmetric extensions are essential in quantum mechanics, providing a lens to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a recognized method for handling symmetric extensions, it grapples with computational constraints, especially due to the large real parameters in generalized qudit systems. In this study, we introduce an approach that adeptly leverages permutation symmetry. By fine-tuning the SDP problem for detecting $ k $-symmetric extensions, our method markedly diminishes the searching space dimensionality and trims the number of parameters essential for positive definiteness tests. This leads to an algorithmic enhancement, reducing the complexity from $ O(d^{2k}) $ to $ O(k^{d^2}) $ in the qudit $ k $-symmetric extension scenario. Additionally, our approach streamlines the process of verifying the positive definiteness of the results. These advancements pave the way for deeper insights into quantum correlations, highlighting potential avenues for refined research and innovations in quantum information theory.

quant-ph↗

arXiv2022

Detecting Entanglement by Pure Bosonic Extension

In the realm of quantum information theory, the detection and quantification of quantum entanglement stand as paramount tasks. The relative entropy of entanglement (REE) serves as a prominent measure of entanglement, with extensive applications spanning numerous related fields. The positive partial transpose (PPT) criterion, while providing an efficient method for the computation of REE, unfortunately, falls short when dealing with bound entanglement. In this study, we propose a method termed "pure bosonic extension" to enhance the practicability of $k$-bosonic extensions, which approximates the set of separable states from the "outside", through a hierarchical structure. It enables efficient characterization of the set of $k$-bosonic extendible states, facilitating the derivation of accurate lower bounds for REE. Compared to the Semi-Definite Programming (SDP) approach, such as the symmetric/bosonic extension function in QETLAB, our algorithm supports much larger dimensions and higher values of extension $k$.

quant-ph↗

arXiv2022

Maximum entropy methods for quantum state compatibility problems

Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state compatibility problem asks whether there exists a density matrix $\rho$ compatible with some given measurement results. Such a compatibility problem can be naturally formulated as a semidefinite programming (SDP), which searches directly for the existence of a $\rho$. However, for large system dimensions, it is hard to represent $\rho$ directly, since it needs too many parameters. In this work, we apply MaxEnt to solve various quantum state compatibility problems, including the quantum marginal problem. An immediate advantage of the MaxEnt method is that it only needs to represent $\rho$ via a relatively small number of parameters, which is exactly the number of the operators measured. Furthermore, in case of incompatible measurement results, our method will further return a witness that is a supporting hyperplane of the compatible set. Our method has a clear geometric meaning and can be computed effectively with hybrid quantum-classical algorithms.

quant-ph↗

arXiv2018

Symmetric vs. bosonic extension for bipartite states

A bipartite state $\rho^{AB}$ has a $k$-symmetric extension if there exists a $k+1$-partite state $\rho^{AB_1B_2\ldots B_k}$ with marginals $\rho^{AB_i}=\rho^{AB}, \forall i$. The $k$-symmetric extension is called bosonic if $\rho^{AB_1B_2\ldots B_k}$ is supported on the symmetric subspace of $B_1B_2\ldots B_k$. Understanding the structure of symmetric/bosonic extension has various applications in the theory of quantum entanglement, quantum key distribution and the quantum marginal problem. In particular, bosonic extension gives a tighter bound for the quantum marginal problem based on seperability. In general, it is known that a $\rho^{AB}$ admitting symmetric extension may not have bosonic extension. In this work, we show that when the dimension of the subsystem $B$ is $2$ (i.e. a qubit), $\rho^{AB}$ admits a $k$-symmetric extension if and only if it has a $k$-bosonic extension. Our result has an immediate application to the quantum marginal problem and indicates a special structure for qubit systems based on group representation theory.

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arXiv2017

Quantum Spacetime on a Quantum Simulator

We experimentally simulate the spin networks -- a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra comprises spin networks. In this initial attempt to study quantum spacetime by quantum information processing, on a four-qubit nuclear magnetic resonance quantum simulator, we simulate the basic module -- comprising five quantum tetrahedra -- of the interactions of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulate their interactions, our experiment serves as the basic module that represents the Feynman diagram vertex in the spin-network formulation of quantum spacetime.

quant-ph↗

arXiv2017

Quantum State Tomography for Generic Pure States

We show that a generic $N$-qudit pure quantum state is uniquely determined by only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices. Therefore we give a method to uniquely determine a generic $N$-qudit pure state of dimension $D=d^N$ with $O(D)$ local measurements, which is an improvement comparing with the previous known approach using $O(D\log^2 D)$ or $O(D\log D)$ measurements.

quant-ph↗

arXiv2017

Random Invariant Tensors

Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon of `concentration of measure', saying that for any bipartition, the expected value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimension goes to infinity. This is also true even when the average is over the invariant subspace instead of the whole space for $4-$valent tensors, although its entropy deficit is divergent. One might expect that for $n\geq 5$, $n-$valent random invariant tensor would behavior similarly. However, we show that, the expected entropy deficit of reduced density matrix of such $n-$valent random invariant tensor from maximum, is not divergent but a finite number. Under some special situation, the number could be even smaller than half a bit, which is the deficit of random pure state over the whole Hilbert space from maximum.

quant-ph↗

arXiv2017

Local density matrices of many-body states in the constant weight subspaces

Let $V=\bigotimes_{k=1}^{N} V_{k}$ be the $N$ spin-$j$ Hilbert space with $d=2j+1$-dimensional single particle space. We fix an orthonormal basis $\{|m_i\rangle\}$ for each $V_{k}$, with weight $m_i\in \{-j,\ldots j\}$. Let $V_{(w)}$ be the subspace of $V$ with a constant weight $w$, with an orthonormal basis $\{|m_1,\ldots,m_N\rangle\}$ subject to $\sum_k m_k=w$. We show that the combinatorial properties of the constant weight condition imposes strong constraints on the reduced density matrices for any vector $|\psi\rangle$ in the constant weight subspace, which limits the possible entanglement structures of $|\psi\rangle$. Our results find applications in the overlapping quantum marginal problems, quantum error-correcting codes, and the spin-network structures in quantum gravity.

quant-ph↗

arXiv2016

Invariant Perfect Tensors

Invariant tensors are states in the SU(2) tensor product representation that are invariant under the SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors recently has attracted a lot of attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is a $n$-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPT. For bivalent tensors, the invariant perfect tensor is the unique singlet state for each local dimension. The trivalent invariant perfect tensor also exists and is uniquely given by Wigner's $3j$ symbol. However, we show that, surprisingly, there does not exist four-valent invariant perfect tensors for any dimension. On the contrary, when the dimension is large, almost all invariant tensors are perfect asymptotically, which is a consequence of the phenomenon of concentration of measure for multipartite quantum states.

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