You have to check that. A good entanglement measure is usually an entanglement monotone. Besides, each entanglement measure could have its own properties. A simple example is the relative entropy of entanglement which is joint convex， but most of others have not this property.

Thanks C.-S. Yu. You are right, I need to check case by case. But I wanted to know is there something in the literature already,that I am missing, which can reduce my effort. So I am rephrasing, what I meant.

Yes, It has been postulated that all good entanglement measures must be LOCC monotone. In my case the channel looks like a global one but decreases the entanglement measured in terms of entanglement of formation or relative entropy of entanglement or negativity. But other measures may or may not decrease. I wanted to know, are there other measures which may be intermediate among the above listed three in terms of properties, which will decrease under this channel? Or in other terms, can I have a necessary and sufficient criterion which will tell whether a global channel unlike LOCC must decrease the entanglement measured by any good measure? This will be helpful for me.

Regards,

Uttam

Interesting question!