Efficient $k$-separability criteria for mixed multipartite quantum states

Abstract

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots ,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.

6 pages, 4 figures

References in corpus (13)

• Entanglement detection
• Quantum information with Gaussian states
• Deterministic secure direct communication using GHZ states and swapping quantum entanglement
• Covariance matrices and the separability problem
• Entanglement of spin waves among four quantum memories
• Unifying several separability conditions using the covariance matrix criterion
• Hierarchies of multi-partite entanglement
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations
• Two Local Observables are Sufficient to Characterize Maximally Entangled States of N Qubits
• Separability criteria for several classes of $n$-partite quantum states
• Verifying multi-partite mode entanglement of W states
• Detection of multipartite entanglement with two-body correlations

Cited by in corpus (31)

• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states
• Separability criteria via sets of mutually unbiased measurements
• Parameterized multipartite entanglement measures
• Detection of multipartite entanglement via quantum Fisher information
• Criteria for non-$k$-separability of $n$-partite quantum states
• Hierarchy of multipartite nonlocality in the nonsignaling scenario
• Separability criteria via some classes of measurements
• Lower bounds of concurrence for $N$-qubit systems and the detection of $k$-nonseparability of multipartite quantum systems
• Entanglement resource theory of quantum channel
• A $(k+1)$-partite entanglement measure of $N$-partite quantum states
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Inherent quantum resources in stationary spin chains
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Detection of the quantum states containing at most $k-1$ unentangled particles
• Detecting Tripartite Steering via Quantum Entanglement
• Detection of tripartite entanglement based on principal basis matrix representations
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• The verification of a requirement of entanglement measures
• Multipartite entanglement detection via generalized Wigner-Yanase skew information
• Necessary and sufficient product criteria for quantum states via the rank of realignment matrix of density matrix
• Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors
• On the non-$k$-separability of Dicke class of states and $N$-qudit W states
• Entanglement hierarchies in multipartite scenarios
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• A Note on Hierarchy of Quantum Measurement Incompatibilities
• Methods of constructing superposition measures
• Quantum Separability Criteria Based on Symmetric Measurements