Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy

Abstract

Entanglement Rényi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement Rényi-$\alpha$ entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-$\alpha$ entropy and some other entanglement measures.

arXiv comment12 pages, 4 figures, published version

References in corpus (52)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Distributed Entanglement
• Quantifying Entanglement
• The logarithmic negativity: A full entanglement monotone that is not convex
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement Measures under Symmetry
• "Squashed Entanglement" - An Additive Entanglement Measure
• The asymptotic entanglement cost of preparing a quantum state
• Concurrence of arbitrary dimensional bipartite quantum states
• Entanglement of formation for symmetric Gaussian states
• The entanglement cost under operations preserving the positivity of partial transpose
• Computing quantum discord is NP-complete
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• The Entanglement of Formation for Isotropic States
• Concurrence of mixed multi-partite quantum states
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• An observable entanglement measure for unknown mixed quantum states
• General monogamy relation for the entanglement of formation in multiqubit systems
• Entanglement of Formation of Bipartite Quantum States
• Entanglement cost of mixed states
• Family of Concurrence Monotones and its Applications
• Lower bounds on concurrence and separability conditions
• Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
• Entanglement for rank-2 mixed states
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Quantum phases with differing computational power
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Lower Bound on Entanglement of Formation for the Qubit-Qudit System
• Estimating entanglement monotones with a generalization of the Wootters formula
• Mixedness in Bell-violation vs. Entanglement of Formation
• Topological Rényi entropy after a quantum quench
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• Entanglement Rényi $\alpha$-entropy
• Mixed State Entanglement of Assistance and the Generalized Concurrence
• Distribution of G-concurrence of random pure states
• A comparison of old and new definitions of the geometric measure of entanglement
• Concurrence-based entanglement measure for Werner States
• Local convertibility and the quantum simulation of edge states in many-body systems
• A Class of Special Matrices and Quantum Entanglement
• Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
• Lower Bound of Concurrence and Distillation for Arbitrary Dimensional Bipartite Quantum States
• R Function Related to Entanglement of Formation
• Lower Bound of Concurrence Based on Positive Maps
• Improved lower and upper bounds for entanglement of formation
• Tight Bounds for the Entanglement of Formation of Gaussian States
• Constrained bounds on measures of entanglement
• A new bound of concurrence

Cited by in corpus (6)

• How much entanglement can be created in a closed system?
• Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$\alpha$ entropy
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Experimental Examination of Entanglement Estimates
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Transmission of coherent information at the onset of interactions