What’s the latest on cross-shard communication?

I know that this doesn’t matter until Phase 2 of Serenity but is there any updated documentation on how cross-shard communication will work? Will a transaction involving data across multiple shards have a significant impact on UX (i.e. will it take a long time?)?

Edit: found this discussion on ETH research https://ethresear.ch/t/cross-shard-receipt-and-hibernation-waking-anti-double-spending/4748

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