# Are entanglement breaking channels of any use?

As the name suggests, an entanglement breaking channel $$\Phi$$ is such that $$(Id \otimes \Phi)[\rho]$$ is always separable, even when $$\rho$$ is entangled. Won't such channels be useless, as they destroy entanglement? Does it make sense to say a channel that is more "entanglement breaking" is more useless?

• Whether something is "useless" or not depends on your objective. If your goal is to prepare a separable state, then an entanglement breaking channel is useful. Moreover, entanglement breaking channel models a large class of processes wherein we measure the input state and based on the measurement outcome prepare an output state. This encompasses tasks that are part of many experiments performed in practice. Aug 25 at 18:29