Epsilon-measures of entanglement

Abstract

We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate the amount of entanglement in a state that is only partially known. We show that many properties of the original measure are inherited by the family, in particular weak monotonicity under transformations applied by means of Local Operations and Classical Communication (LOCC). On the other hand, they may increase on average under stochastic LOCC. Remarkably, the epsilon-version of a convex entanglement measure is continuous even if the original entanglement measure is not, so that the epsilon-version of an entanglement measure may be actually considered a smoothed version of it.

9 pages, 3 figures

References in corpus (9)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Distributed Entanglement
• Quantifying Entanglement
• The logarithmic negativity: A full entanglement monotone that is not convex
• Entanglement Measures and Purification Procedures
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Universal resources for measurement-based quantum computation
• Classical simulation versus universality in measurement based quantum computation
• Fundamentals of universality in one-way quantum computation

Cited by in corpus (6)

• Universal quantum computation with little entanglement
• A Generalization of Quantum Stein's Lemma
• Entanglement cost in practical scenarios
• Universal resources for approximate and stochastic measurement-based quantum computation
• Epsilon-smooth measure of coherence
• Distance-based measures and Epsilon-measures for measurement-based quantum resources