Polynomial Monogamy Relations for Entanglement Negativity

Abstract

The notion of non-classical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations---the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under LOCC, and derive a necessary and sufficient inequality which, for the first time, is a non-linear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.

5 pages, 3 figures

References in corpus (8)

• Entanglement in continuous variable systems: Recent advances and current perspectives
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Should Entanglement Measures be Monogamous or Faithful?
• Monogamy equalities for qubit entanglement from Lorentz invariance
• Monogamy and ground-state entanglement in highly connected systems
• Negativity as a distance from a separable state

Cited by in corpus (13)

• Monogamy of entanglement without inequalities
• Multipartite Entanglement Measure and Complete Monogamy Relation
• Monogamy of the Entanglement of Formation
• Any entanglement of assistance is polygamous
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Generalized Entanglement Measure for Continuous Variable Systems
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Realization of the tradeoff between internal and external entanglement
• Correlation constraints and the Bloch geometry of two qubits
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Trade-off relations of l_1-norm coherence for multipartite systems
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures