entanglementmonotones

Entanglement monotones are quantities that characterize the entanglement of a quantum state and are non-increasing under certain quantum operations. These operations typically represent the loss of entanglement that can occur during physical processes. The concept is crucial in quantum information theory for understanding and quantifying how much entanglement is present in a system and how it behaves over time or under interaction with an environment.

A key feature of an entanglement monotone is its monotonic decrease. For instance, if a bipartite quantum state undergoes a local operation and classical communication (LOCC) process, any entanglement monotone associated with that state will either stay the same or decrease. This property makes them reliable measures, as they cannot be artificially increased through decoherence or entanglement distillation protocols that are not designed to create entanglement from scratch.

Different entanglement monotones exist for various types of entanglement and for different classes of quantum states. For example, measures like entanglement entropy are used for pure bipartite states, while others are developed for mixed states or multi-partite systems. The choice of an entanglement monotone often depends on the specific problem being addressed, such as determining the capacity of a quantum channel for transmitting entanglement or analyzing the entanglement dynamics in a quantum computer. Researchers use these monotones to set bounds on achievable performance in quantum communication and computation tasks.