A new class of entanglement measures

Abstract

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.

Revised version accepted by J Math Phys, 12 pages, LaTeX, contains Sections 1-5 & 7 of the previous version. The previous Section 6 is now in quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/0105017

References in corpus (3)

• Limits for entanglement measures
• A uniqueness theorem for entanglement measures
• A separability criterion for density operators

Cited by in corpus (12)

• Further results on the cross norm criterion for separability
• The Uniqueness Theorem for Entanglement Measures
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Convex geometry of quantum resource quantification
• Operational quantification of continuous-variable quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Perspectives for a mixed two-qubit system with binomial quantum states
• Some notes on the robustness of k-coherence and k-entanglement
• Accessible bounds for general quantum resources
• Entanglement Measures with Asymptotic Weak-Monotonicity as Lower (Upper) Bound for the Entanglement of Cost (Distillation)
• Smallest state spaces for which bipartite entangled quantum states are separable
• Entanglement in the interaction between two quantum oscillator systems