Entanglement of Formation of Bipartite Quantum States

Abstract

We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.

arXiv comment4 pages

References in corpus (28)

• 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
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement of a Pair of Quantum Bits
• Scaling of Entanglement close to a Quantum Phase Transitions
• Quantum Phase Transitions and Bipartite Entanglement
• Entanglement Measures under Symmetry
• Characterizing Entanglement
• Entangled Quantum States of Magnetic Dipoles
• Concurrence of arbitrary dimensional bipartite quantum states
• Entanglement of formation for symmetric Gaussian states
• Concurrence of mixed bipartite quantum states in arbitrary dimensions
• The Entanglement of Formation for Isotropic States
• Some Properties of the Computable Cross Norm Criterion for Separability
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Variational Characterisations of Separability and Entanglement of Formation
• Entanglement cost of mixed states
• The generalized partial transposition criterion for separability of multipartite quantum states
• Generalized reduction criterion for separability of quantum states
• Lower Bound on Entanglement of Formation for the Qubit-Qudit System
• Test for entanglement using physically observable witness operators and positive maps
• Entanglement of Formation for a Class of Quantum States
• Strong superadditivity of the entanglement of formation follows from its additivity
• Entanglement for a two-parameter class of states in $2\otimes n$ quantum system
• Entanglement of 2xK quantum systems
• A Class of Special Matrices and Quantum Entanglement

Cited by in corpus (80)

• Quantum entanglement
• Entanglement detection
• Sudden Birth Versus Sudden Death of Entanglement in Multipartite Systems
• Quantifying entanglement resources
• Optimal entanglement criterion for mixed quantum states
• Violation of monogamy inequality for higher-dimensional objects
• Lower bounds on concurrence and separability conditions
• Systematic errors in current quantum state tomography tools
• Unifying several separability conditions using the covariance matrix criterion
• Separability criteria and bounds for entanglement measures
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Roofs and Convexity
• A lower bound of concurrence for multipartite quantum states
• Hybrid photonic entanglement: Realization, characterization and applications
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Lower Bounds of Concurrence for Tripartite Quantum Systems
• Abrupt Changes in the Dynamics of Quantum Disentanglement
• Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations
• Lower bounds on entanglement measures from incomplete information
• Quantifying entanglement with covariance matrices
• An Introduction to Quantum Entanglement: a Geometric Approach
• Finite-time destruction of entanglement and non-locality by environmental influences
• Bipartite entanglement of quantum states in a pair basis
• Entanglement detection via tighter local uncertainty relations
• Entanglement dynamics of three-qubit states in noisy channels
• Local Unitary Equivalence of Arbitrary Dimensional Bipartite Mixed Quantum States
• A new parameterized entanglement monotone
• Experimental Determination of Entanglement for Arbitrary Pure States
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Monogamy inequality for any local quantum resource and entanglement
• Detecting and estimating continuous-variable entanglement by local orthogonal observables
• Novel Schemes for Directly Measuring Entanglement of General States
• Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
• A Class of Bound Entangled States
• Classification of multipartite entanglement containing infinitely many kinds of states
• Upper bound of the fully entangled fraction
• A Study of Teleportation and Super Dense Coding capacity in Remote Entanglement Distribution
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• Estimating multipartite entanglement measures
• Entanglement of formation for a class of $(2\otimes d)$-dimensional systems
• R Function Related to Entanglement of Formation
• Lower Bound of Concurrence Based on Positive Maps
• Thermal entanglement witness for materials with variable local spin lengths
• Three-tangle for high-rank mixed states
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Parameterized Bipartite Entanglement Measure
• Improved lower and upper bounds for entanglement of formation
• Monogamy inequality for entanglement and local contextuality
• Entanglement of Multipartite Schmidt-correlated States
• Stable and metastable freezing of classical correlations in qutrits
• Constrained bounds on measures of entanglement
• An Upper Bound of Fully Entangled Fraction of Mixed States
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Evaluation of entanglement measures by a single observable
• Measurement-induced nonlocality over two-sided projective measurements
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• A generic framework for genuine multipartite entanglement detection
• The criterion for maximally entangled four-qubit state
• Estimating Parameterized Entanglement Measure
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Additivity of entanglement of formation via entanglement-breaking space
• Method for measuring the entanglement of formation for arbitrary-dimensional pure states
• D-concurrence bounds for pair coherent states
• A Note on Quantum Entanglement and PPT
• Embedded Quantum Correlations in thermalized quantum Rabi systems
• Tripartite genuinely entangled states from entanglement-breaking subspaces
• Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations
• Quantitative entanglement witnesses of Isotropic- and Werner-class via local measurements
• Equation of motion for multiqubit entanglement in multiple independent noisy channels
• Dissipative dynamics of atom-field entanglement in the ultrastrong-coupling regime
• Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations
• Separability of Hermitian Tensors and PSD Decompositions
• Local unitary equivalence of arbitrary-dimensional multipartite quantum states
• Entanglement Generation and Dynamics for a Bose-Hubbard model in a Double-Well Potential
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Entanglement of formation for qubit-qudit system using partition of qudit sytem into a set of qubit system
• Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities
• Weak Schmidt decomposition and generalized Bell basis related to Hadamard matrices
• Identifying local unitary equivalence based on reduction of quantum states