Partial separability and entanglement criteria for multiqubit quantum states

Abstract

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-Żukowski criterion and the Dür-Cirac criterion), and also by showing their great noise robustness for a variety of multiqubit states, including N-qubit GHZ states and Dicke states. Furthermore, for N greater than or equal to 3 they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only N+1. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the anti-diagonal matrix elements of a state in terms of its diagonal matrix elements.

25 pages, 3 figures. v4: published version

References in corpus (37)

• Scalable multi-particle entanglement of trapped ions
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Unextendible Product Bases and Bound Entanglement
• Classification of mixed three-qubit states
• Witnessing multipartite entanglement
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Bell-type inequalities to detect true n-body non-separability
• Classification of multi-qubit mixed states: separability and distillability properties
• Separability and distillability of multiparticle quantum systems
• Entanglement Detection in the Stabilizer Formalism
• Bell inequality, Bell states and maximally entangled states for n qubits
• Multipartite entanglement in spin chains
• Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations
• A four-party unlockable bound-entangled state
• Toolbox for entanglement detection and fidelity estimation
• Entanglement molecules
• Separability properties of tripartite states with UxUxU-symmetry
• Sufficient conditions for three-particle entanglement and their tests in recent experiments
• Multipartite bound entangled states that violate Bell's inequality
• Quadratic Bell inequalities as tests for multipartite entanglement
• Do all pure entangled states violate Bell's inequalities for correlation functions?
• Bell's inequalities for states with positive partial transpose
• Investigating three qubit entanglement with local measurements
• Configuration of separability and tests for multipartite entanglement in Bell-type experiments
• Note on Separability of the Werner states in arbitrary dimensions
• Multiparticle entanglement and its experimental detection
• Bell's inequalities with realistic noise for polarization-entangled photons
• Local commutativity versus Bell inequality violation for entangled states and versus non-violation for separable states
• N-Partite Separability Inequalities Exponentially Stronger Than Local Reality inequalities
• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices
• Detection of multipartite entanglement with two-body correlations
• Detection of N-particle entanglement with generalized Bell inequalities
• Multiqubit entanglement witness
• Strengthened Bell inequalities for orthogonal spin directions
• Robustness of multiparty nonlocality to local decoherence
• Observables suitable for restricting the fidelity to multipartite maximally entangled states

Cited by in corpus (71)

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• Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
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• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Postulates for measures of genuine multipartite correlations
• Purification of genuine multipartite entanglement
• Sharing quantum nonlocality and genuine nonlocality with independent observables
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Detection of genuine tripartite entanglement by multiple sequential observers
• Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side
• Correlation tensor criteria for genuine multiqubit entanglement
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Fermionic systems for quantum information people
• Partial separability revisited: Necessary and sufficient criteria
• Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states
• Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• A study of separability criteria for mixed three-qubit states
• Lorentz invariance of entanglement classes in multipartite systems
• Anonymous Quantum Nonlocality
• Entanglement and communication-reducing properties of noisy N-qubit states
• Multipartite entanglement in a microwave frequency comb
• Proving the Generation of Genuine Multipartite Entanglement in a Single-Neutron Interferometer Experiment
• Entangling three identical particles via spatial overlap
• Parts and Wholes. An Inquiry into Quantum and Classical Correlations
• The classification of multipartite quantum correlation
• Criteria for non-$k$-separability of $n$-partite quantum states
• Hierarchy of multipartite nonlocality in the nonsignaling scenario
• Separability in terms of a single entanglement witness
• Efficient Test to Demonstrate Genuine Three Particle Nonlocality
• Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification
• Polynomial method to study the entanglement of pure N-qubit states
• Graph Picture of Linear Quantum Networks and Entanglement
• Construction of genuine multipartite entangled states
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix
• Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states
• Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model
• A Computable Criterion for Partial Entanglement in Continuous Variable Quantum Systems
• User-friendly confidence regions for quantum state tomography
• Alternatives of entanglement depth and metrological entanglement criteria
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• On the convex cones arising from classifications of partial entanglement in the three qubit system
• The quantum separability problem is a simultaneous hollowisation matrix analysis problem
• Werner gap in presence of simple coloured noise
• Inherent quantum resources in stationary spin chains
• Stretching the limits of multiparticle entanglement
• Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors
• There exist infinitely many kinds of partial separability/entanglement
• Heuristic for estimation of multiqubit genuine multipartite entanglement
• Multipartite entanglement detection via generalized Wigner-Yanase skew information
• On the non-$k$-separability of Dicke class of states and $N$-qudit W states
• Dicke subsystems are entangled
• Classifying Entanglement by Algebraic Geometry
• Device-Independent Test for Genuine Multipartite Entanglement
• Quantum Advantage in Distributed Sensing with Noisy Quantum Networks
• Variational-toolbox-based separability detection of multiqubit states
• Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
• Entanglement-Constrained Quantum Metrology: Rapid Low-Entanglement Gains, Tapered High-Level Growth
• Criteria for partial entanglement of three qubit states arising from distributive rules
• Study of decoherence of entangled states made up of two basic states in a linear chain of three qubits
• On the separability criterion of bipartite states with certain non-Hermitian operators
• Embeddings of spaces of quregisters into special linear groups
• About Factorization of Quantum States with Few Qubits