Looks like this could be "More Than Time Or Distance", indeed included in Vacuum Diagrams.
Some of the key points:
My one-woman flitter dropped into the luminous wreckage of an old supernova. I peered into the folded-out depths of the dead star, hoarding details like coins for Timothy.
Discovers Faster-Than-Light communication:
I worked out the implications of that, and then I leaned carefully against a low pillar and breathed deep enough to mist up my face plate.
Think about it. Ring A was talking to ring B, which got the message delayed by a nanosecond. Each ring was a light nanosecond across. And the rings were placed a hundred light nanoseconds apart.
So all the delay was in the structure of the rings — and the communication between them was instantaneous.
My face plate fogged a bit more. Instantaneous communication: it was a technological prize second only in value to the hyperdrive itself…
The secret had to be quantum inseparability. When a single object is split up, its components can still communicate instantaneously. That’s high school stuff, Bell’s theorem from the twentieth century. But, everyone had thought, you couldn’t use the effect to send meaningful messages.
Competing with another alien:
And at just that moment, in walked a giant alien monster with a zap gun. Wouldn’t you know it?
Ends with an act of nobility by the losing alien:
Even the Statue was company. “You have been a worthy… opponent.”
“You’re repeating yourself,” I said rudely.
“My ship is at… the planet’s nearer pole, one day’s journey from here. You may be able to adapt its life system to your purposes.”
“Ah… thank you. Why?”
“Because you would probably find it anyway. And I hope your species will… be tolerant of mine in the future.”