Inclusion relations among separability criteria

Abstract

We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria is in such a way numerically elucidated. We also quantify, for a bipartite system of arbitrary dimension, the proportion of states $\rho$ that can be distilled according to a definite criterion. Our work can be regarded as a complement to the recent review paper by B. Terhal [Theor. Comp. Sci. {\bf 287} (2002) 313]. Some questions posed there receive an answer here.

Submitted for publication

References in corpus (24)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• On the volume of the set of mixed entangled states
• Information-theoretic aspects of quantum inseparability of mixed states
• Information and Computation: Classical and Quantum Aspects
• Negative entropy and information in quantum mechanics
• Induced measures in the space of mixed quantum states
• Distinguishing separable and entangled states
• Maximizing the entanglement of two mixed qubits
• Separable states are more disordered globally than locally
• On the volume of the set of mixed entangled states II
• Maximally entangled mixed states in two qubits
• Nonextensive Thermostatistics and the H-Theorem
• Operational criterion and constructive checks for the separability of low rank density matrices
• Composed ensembles of random unitary matrices
• Conditional entropies and their relation to entanglement criteria
• Conditional q-Entropies and Quantum Separability: A Numerical Exploration
• A priori Probabilities of Separable Quantum States
• Entanglement and nonextensive statistics
• Nonadditive measure and quantum entanglement in a class of mixed states of N^n-system
• On the Entanglement Properties of Two-Rebits Systems
• Exact Bures Probabilities that Two Quantum Bits are Classically Correlated
• Some Features of the Conditional $q$-Entropies of Composite Quantum Systems
• A nonextensive critical phenomenon scenario for quantum entanglement

Cited by in corpus (4)

• An Introduction to Quantum Entanglement: a Geometric Approach
• Rank three bipartite entangled states are distillable
• Eigenvalues, Separability and Absolute Separability of Two-Qubit States
• Local uncertainty relations serving as measures of entanglement in a bipartite two-level system