Optimization of device-independent witnesses of entanglement depth from two-body correlators

Abstract

In a recent work [A. Aloy et al. arXiv:1807:06027 (2018)] we have considered the characterization of entanglement depth, from a device-independent perspective, in a quantum many-body system. We have shown that the inequalities introduced in [J. Tura et al. Science 344 1256 (2014)] can be used to obtain device-independent witnesses of entanglement depth and that they enjoy two key properties that allow to compute their $k$-producibility bounds more efficiently for larger system sizes, as well as yielding experimentally-friendlier device-independent witnesses of entanglement depth: they involve at most two-body correlators and they are permutationally invariant. While the main aim of our previous work was to illustrate the main ideas and applicability of the method, here we outline the details and complement its findings with detailed analysis and further case studies. Specifically, we consider the problem of finding the $k$-producible bounds of such DIWEDs under different assumptions. Not surprisingly, with the weakest assumptions, we can compute $k$-producible bounds only for relatively small number of parties; however we can still learn interesting features from these solutions that motivate the search on larger systems under the assumption that these features persist. This allows us to tackle the case where the system size eventually reaches the thermodynamic limit.

arXiv comment16 pages (14.2 + appendices), 8 figures

References in corpus (65)

• Separability Criterion for Density Matrices
• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Device-independent security of quantum cryptography against collective attacks
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Multidimensional quantum entanglement with large-scale integrated optics
• Bounding the set of quantum correlations
• Entanglement and Extreme Spin Squeezing
• A complete family of separability criteria
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Separability criteria for genuine multiparticle entanglement
• Challenging local realism with human choices
• Device-independent witnesses of genuine multipartite entanglement
• Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in a Bose-Einstein condensate
• Detecting multiparticle entanglement of Dicke states
• Entanglement detection via mutually unbiased bases
• Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
• Bell Correlations in a Bose-Einstein Condensate
• Almost quantum correlations
• Detecting non-locality in multipartite quantum systems with two-body correlation functions
• All Pure Bipartite Entangled States can be Self-Tested
• Entanglement between two spatially separated atomic modes
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Device-independent entanglement quantification and related applications
• Connes' embedding problem and Tsirelson's problem
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Geometry of the set of quantum correlations
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Tsirelson's problem and Kirchberg's conjecture
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Permutationally invariant state reconstruction
• Multipartite entanglement measures
• Spin squeezing inequalities for arbitrary spin
• Self-testing of binary observables based on commutation
• Bell inequalities tailored to maximally entangled states
• Device-independent entanglement certification of all entangled states
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Semi-device-independent bounds on entanglement
• Device-independent demonstration of genuine multipartite entanglement
• Machine Learning Bell Nonlocality in Quantum Many-body Systems
• Nonlocality in many-body quantum systems detected with two-body correlators
• Hierarchies of multi-partite entanglement
• Device-independent witnesses of entanglement depth from two-body correlators
• Four-qubit entangled symmetric states with positive partial transpositions
• Entangled symmetric states of N qubits with all positive partial transpositions
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Bell correlations depth in many-body systems
• Multipartite entanglement detection with minimal effort
• Partial separability revisited: Necessary and sufficient criteria
• Device-independent detection of genuine multipartite entanglement for all pure states
• Genuine Multipartite Entanglement without Multipartite Correlations
• Experimental certification of millions of genuinely entangled atoms in a solid
• Bounding the set of classical correlations of a many-body system
• An improved semidefinite programming hierarchy for testing entanglement
• Bell correlations in a many-body system with finite statistics
• Energy as witness of multipartite entanglement in spin clusters
• Best Separable Approximation of multipartite diagonal symmetric states
• Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth
• Entanglement and Nonlocality in Diagonal Symmetric States of $N$-qubits
• Bell correlations at finite temperature
• Nonlocality with ultracold atoms in a lattice
• Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses
• Genuine $N$-partite entanglement without $N$-partite correlation functions
• Mutually Unbiased Bases and Bound Entanglement
• Characterizing the width of entanglement

Cited by in corpus (22)

• Bounds on the capacity and power of quantum batteries
• Semidefinite programming relaxations for quantum correlations
• Device-independent witnesses of entanglement depth from two-body correlators
• One- and two-axis squeezing via laser coupling in an atomic Fermi-Hubbard model
• One-axis twisting as a method of generating many-body Bell correlations
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• Accelerating many-body entanglement generation by dipolar interactions in the Bose-Hubbard model
• Detecting Bell correlations in multipartite non-Gaussian spin states
• Enhancing quantum state tomography via resource-efficient attention-based neural networks
• Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions
• Certificates of quantum many-body properties assisted by machine learning
• Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads
• Symmetric quantum states: a review of recent progress
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Bell inequalities for nonlocality depth
• Inherent quantum resources in stationary spin chains
• Non-stabilizerness in quantum-enhanced metrological protocols
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Multiqubit monogamy relations beyond shadow inequalities
• Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system