Characterizing entanglement with global and marginal entropic measures

Abstract

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entaglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion.

6 pages, 5 color figures in low resolution due to oversizing problems; to get the original high-resolution figures please contact the authors. Minor changes, final version

References in corpus (11)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• On the volume of the set of mixed entangled states
• Maximal entanglement versus entropy for mixed quantum states
• Maximizing the entanglement of two mixed qubits
• Separable states are more disordered globally than locally
• Maximally entangled mixed states of two qubits
• Maximally entangled mixed states in two qubits
• Generalized entropic criterion for separability

Cited by in corpus (21)

• Extremal entanglement and mixedness in continuous variable systems
• Entanglement of Dirac fields in non-inertial frames
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Continuous variable entanglement sharing in non-inertial frames
• Determination of continuous variable entanglement by purity measurements
• Complete hierarchies of efficient approximations to problems in entanglement theory
• Concurrence vs. purity: Influence of local channels on Bell states of two qubits
• Frustration, Entanglement, and Correlations in Quantum Many Body Systems
• Entanglement, Purity, and Information Entropies in Continuous Variable Systems
• Complementarity relations for multi-qubit systems
• Statistical distribution of the local purity in a large quantum system
• On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
• Entanglement in the dispersive interaction of trapped ions with a quantized field
• Faithful geometric measures for genuine tripartite entanglement
• Complementarity and Entanglement in Quantum Information Theory
• Correlation constraints and the Bloch geometry of two qubits
• Fundamental noisy multiparameter quantum bounds
• Bounds on bipartite entanglement from fixed marginals
• The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Entanglement of bipartite states and quantum teleportation: an introduction