Characterizing the entanglement of symmetric many-particle spin-1/2 systems

Abstract

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to investigate many-particle entanglement when the state of the system possesses sufficient symmetry. In this paper, we present a practical method for efficiently computing various bipartite entanglement measures for states in the symmetric subspace and perform these calculations for $N\sim 10^3$. By considering all possible bipartite splits, we construct a picture of the multiscale entanglement in large symmetric systems. In particular, we characterize dynamically generated spin-squeezed states by comparing them to known reference states (e.g., GHZ and Dicke states) and new families of states with near-maximal bipartite entropy. We quantify the trade-off between the degree of entanglement and its robustness to particle loss, emphasizing that substantial entanglement need not be fragile.

arXiv commentUpdated version reflects changes made in January 2003

References in corpus (32)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Three qubits can be entangled in two inequivalent ways
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Conditions for a class of entanglement transformations
• Experimental long-lived entanglement of two macroscopic objects
• Multi-particle entanglement of hot trapped ions
• Many-particle entanglement with Bose--Einstein condensates
• Four qubits can be entangled in nine different ways
• Entanglement and Extreme Spin Squeezing
• Entanglement Measures under Symmetry
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Entanglement of pure states for a single copy
• Dynamics of quantum entanglement
• Limits for entanglement measures
• A potential multipartide entanglement measure
• Classification of multi-qubit mixed states: separability and distillability properties
• Bell inequality, Bell states and maximally entangled states for n qubits
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Quantum Correlations in Two-Boson Wavefunctions
• Evidence for Bound Entangled States with Negative Partial Transpose
• Distillability and partial transposition in bipartite systems
• Robustness of Multi-Party Entanglement
• Spin squeezing via quantum feedback
• Entangled webs: Tight bound for symmetric sharing of entanglement
• Entanglement molecules
• Atom correlations and spin squeezing near the Heisenberg limit: finite system size effect and decoherence
• Robust and Fragile Entanglement of Three Qubits: Relation to Permutation Symmetry

Cited by in corpus (146)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Multi-party entanglement in graph states
• Quantum spin squeezing
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Feedback control of quantum state reduction
• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Entanglement in a second order quantum phase transition
• Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
• Spin squeezing and pairwise entanglement for symmetric multiqubit states
• Spin squeezing and entanglement
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Deterministic Dicke state preparation with continuous measurement and control
• Extracting entanglement from identical particles
• Entanglement in a first order quantum phase transition
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Entanglement Sharing in the Two-Atom Tavis-Cummings Model
• The maximally entangled symmetric state in terms of the geometric measure
• Entanglement constrained by superselection rules
• Robust quantum parameter estimation: coherent magnetometry with feedback
• Sudden vanishing of spin squeezing under decoherence
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Variational-State Quantum Metrology
• Tensor polarizability and dispersive quantum measurement of multilevel atoms
• A measurement-based measure of the size of macroscopic quantum superpositions
• Local asymptotic normality for qubit states
• Entanglement and symmetry in permutation symmetric states
• Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
• Generation of Massive Entanglement Through Adiabatic Quantum Phase Transition in a spinor condensate
• Tavis-Cummings model and collective multi-qubit entanglement in trapped ions
• Collective processes of an ensemble of spin-1/2 particles
• Preparation of Dicke States in an Ion Chain
• Quantum correlation in disordered spin systems: entanglement and applications to magnetic sensing
• Extended Coherence Time with Atom-Number Squeezed Sources
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures
• Entanglement detection in the vicinity of arbitrary Dicke states
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• Continuous phase-space representations for finite-dimensional quantum states and their tomography
• Relations between bosonic quadrature squeezing and atomic spin squeezing
• Entangled symmetric states of N qubits with all positive partial transpositions
• Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems
• Separability of Bosonic Systems
• Macroscopic entanglement of many-magnon states
• Exchange Symmetry and Multipartite Entanglement
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Finite-size scaling exponents and entanglement in the two-level BCS model
• Robustness of multi-qubit entanglement in the independent decoherence model
• Quantifying genuine multipartite correlations and their pattern complexity
• Multi-qubit entanglement engineering via projective measurements
• Entanglement quantification in atomic ensembles
• Classification of Entanglement in Symmetric States
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• Phase space geometry and optimal state preparation in quantum metrology with collective spins
• Differential atom interferometry beyond the standard quantum limit
• Experimental certification of millions of genuinely entangled atoms in a solid
• Entanglement robustness against particle loss in multiqubit systems
• Entanglement and spin squeezing in the three-qubit transverse Ising model
• Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage
• States for phase estimation in quantum interferometry
• Creation of arbitrary Dicke and NOON states of trapped-ion qubits by global addressing with composite pulses
• Optimal quantum tomography of permutationally invariant qubits
• Entanglement in highly symmetric multipartite quantum states
• Protecting and Enhancing Spin Squeezing via Continuous Dynamical Decoupling
• Spin squeezing criterion with local unitary invariance
• Nonlocality of $W$ and Dicke states subject to losses
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Wigner negativity in spin-$j$ systems
• Dissipative Dicke model with non-linear atom-photon interaction
• Dephasing-assisted parameter estimation in the presence of dynamical decoupling
• Artificial quantum-dot Helium molecules: Electronic spectra, spin structures, and Heisenberg clusters
• Random multiparty entanglement distillation
• Multiqubit entanglement witness
• Operational multipartite entanglement classes for symmetric photonic qubit states
• Detecting genuine multipartite entanglement via machine learning
• Locally optimal measurement-based quantum feedback with application to multi-qubit entanglement generation
• Precision Measurements Using Squeezed Spin States via Two-axis Counter-twisting Interactions
• Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices
• Collective randomized measurements in quantum information processing
• Dynamics of dissipative Bose-Einstein condensation
• Time evolution of coupled spin systems in a generalized Wigner representation
• Fast computation of spherical phase-space functions of quantum many-body states
• An alternative representation for pure symmetric states of qubits and its applications to entanglement classification
• Genuine Multipartite Correlations Distribution in the Criticality of Lipkin-Meshkov-Glick Model
• Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles
• Asymptotic tensor rank of graph tensors: beyond matrix multiplication
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Extreme depolarization for any spin
• Truncated su(2) moment problem for spin and polarization states
• Quantifying the difference between many-body quantum states
• Entanglement of two distant Bose-Einstein condensates by detection of Bragg-scattered photons
• Eigenstate entanglement in integrable collective spin models
• End-to-end entanglement in Bose-Hubbard chains
• Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states
• Arbitrary control of multiple-qubit systems in the symmetric Dicke subspace
• Dynamics of genuine multipartite correlations in open quantum systems
• Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement
• Collective multipole-like signatures of entanglement in symmetric N-qubit systems
• Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix
• Global Variational Quantum Circuits for Arbitrary Symmetric State Preparation
• Speeding Up Squeezing with a Periodically Driven Dicke Model
• Measurement-induced multipartite-entanglement regimes in collective spin systems
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• Entangled-State Cycles of Atomic Collective-Spin States
• State transformations within entanglement classes containing permutation-symmetric states
• Ordered Measurements of Permutationally-Symmetric Qubit Strings
• Spin Squeezing Property of Weighted Graph States
• Complementarity and Entanglement in Quantum Information Theory
• Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states
• Closing the detection loophole in multipartite Bell experiments with a limited number of efficient detectors
• Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup
• Entanglement Measures for Intermediate Separability of Quantum States
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Dichotomy of entanglement depth for symmetric states
• Equivalence between two-mode spin squeezed states and pure entangled states with equal spin
• Genuine multipartite entanglement verification with convolutional neural networks
• Global multipartite entanglement dynamics in Grover's search algorithm
• Multipartite entanglement in the diagonal symmetric subspace
• Entanglement and spin squeezing properties for three bosons in two modes
• Qubit entanglement in multimagnon states
• Stochastic local operations and classical communication equations and classification of even $n$ qubits
• Maximally genuine multipartite entangled mixed X-states of N-qubits
• Revealing hidden physical nonclassicality with nonnegative polynomials
• On Multiparticle Entanglement via Resonant Interaction between Light and atomic Ensembles
• Heuristic for estimation of multiqubit genuine multipartite entanglement
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Switchable selective interactions in a Dicke Model with Driven Biased term
• Practical implementation of mutually unbiased bases using quantum circuits
• Stability of Flip and Exchange Symmetric Entangled State Classes under Invertible Local Operations
• Witnessing environment dimension through temporal correlations
• Dicke subsystems are entangled
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Bound on entanglement in neural quantum states
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Entangling capabilities of Symmetric two qubit gates
• Evaluating Pauli errors on cluster states by weighted distances
• Characterization and generation of a SQL-beating catlike state through repetitive measurements
• Bounding fidelity in quantum feedback control: theory and applications to Dicke state preparation
• Exact quantification of bipartite entanglement in unresolvable spin ensembles
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
• Decoherence assisted spin squeezing generation in superposition of tripartite GHZ and W states
• Quantum Effects In Low Temperature Bosonic Systems
• Rank-based SLOCC classification for odd n qubits
• Unified monogamy relation of entanglement measures
• Z-States Algebra for a Tunable Multi-Party Entanglement-Distillation Protocol