Evaluation of convex roof entanglement measures

Abstract

We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples

6 pages including 3 figures, 6-page supplement with 2 figures, revtex4; v2: typos corrected, presentation improved, title shortened. For the CoRoNa MATLAB package for convex roof numerical analysis, which has been used for the manuscript, see http://www.mathworks.com/matlabcentral/fileexchange/47823-corona-convex-roof-numerical-analysis

References in corpus (20)

• Entanglement detection
• General Monogamy Inequality for Bipartite Qubit Entanglement
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• A complete family of separability criteria
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Taming multiparticle entanglement
• Concurrence of arbitrary dimensional bipartite quantum states
• Experimental entanglement of a six-photon symmetric Dicke state
• The structure of multidimensional entanglement in multipartite systems
• Estimating entanglement measures in experiments
• Covariance matrices and the separability problem
• Entanglement and permutational symmetry
• Lower bounds on concurrence and separability conditions
• Detecting multipartite entanglement
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Semi-device-independent bounds on entanglement
• A lower bound of concurrence for multipartite quantum states
• Estimating entanglement monotones with a generalization of the Wootters formula
• Lower bounds on entanglement measures from incomplete information

Cited by in corpus (28)

• Entanglement Certification $-$ From Theory to Experiment
• Semidefinite programming relaxations for quantum correlations
• Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Certifying the quantum Fisher information from a given set of mean values: a semidefinite programming approach
• Quantitative bound entanglement in two-qutrit states
• Quantum Wasserstein distance based on an optimization over separable states
• A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
• Interplay among entanglement, measurement incompatibility, and nonlocality
• Introduction to quantum entanglement in many-body systems
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Order $p$ quantum Wasserstein distances from couplings
• Embedded Quantum Correlations in thermalized quantum Rabi systems
• Unified Framework for Calculating Convex Roof Resource Measures
• Quantifying entanglement from the geometric perspective
• Witnessing environment dimension through temporal correlations
• Device-independent certification of desirable properties with a confidence interval
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Entanglement Classification via Single Entanglement Measure
• Entanglement Meter: Estimation of entanglement with single copy in Interferometer
• Entanglement Cost for Steering Assemblages
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• Classification of three-qubit genuine entangled states using concurrence fill
• Interplay of Quantum Resources in Nonlocality Tests
• Graph theoretic quantum contextuality and unextendible Product Bases
• Extremal Steering Assemblages
• Exact quantification of bipartite entanglement in unresolvable spin ensembles
• Strength of statistical evidence for genuine tripartite nonlocality