2025 was arguably the best year of research of my life. Despite it being what I’ve been calling “my year of rest and relaxation”,1: In the gap-year-between-postdoc-and-professor sense, not the femcel+self-medicated-cluster-B+9/11-for-some-reason sense. in this academic year I produced the result in my career that I’m the proudest of: the random purification channel.
It’s been interesting watching this idea proliferate through my community. I doubt this result is going to win any awards or miscellaneous ivory tower points, for reasons both logistical and cultural.2: A representative quote from a review (which I was ecstatic to receive, for the record): “If Mike and Ike were to write another edition of their textbook, random purifications and its application to mixed state tomography as described in this paper would most certainly be in it. Despite all these wonderful consequences, my reason for giving a recommendation of weak accept…” I’m still in love with it, though, since it’s a obvious-in-hindsight observation that dissolves the most difficult problems in my domain. Piles of papers and hundreds of pages become unnecessary with this trick. And the statement of it could be explained in a couple minutes to anyone in my field.3: Theorem. There is a quantum circuit which converts copies of a state to copies of , where is a uniformly random purification of . Note that the purification is the same across all copies. I (regrettably) care deeply about mathematical beauty, but this is the thing I’ve had a part in that has the most of that. And, for the first time in a while, it’s hard for me to downplay my role in the result, because I came up with the idea fully-formed.
What’s interesting is that, with the release of our paper on the random purification channel, a war has broken out over who owns the result. Paper after paper has been shoved on the arXiv to claim intellectual territory, battles fought with non-confrontational language shunted to footnotes and careful elisions. Unusual for academia, the arguments have surfaced beyond paper to person. Several people have told us that various researchers just don’t think that we came up with the critical idea. We aren’t the ones who deserve the credit for the idea, we are merely the popularizers. Honestly, I don’t know what to make of all of this, but it’s an interesting story and I want to talk about it before I lose the fire.
Here’s a non-technical description of the timeline of events. There’s a researcher QW in my field who salami slices; he’s sharp, but instead of focusing on getting the right answers for the problems he studies, he gets the wrong answer over and over again, milking a paper out of it each time. This kind of behavior isn’t rewarded in academia, and especially not a community as small as ours; you can’t cheat the system when everyone knows each other. However, it does accomplish a goal, which is to get a lot of papers in (perhaps not the most well-regarded) journals and conferences and pump up your citation count, which might matter for your career depending on your university. When talking to John about QW’s papers last year, one particular one came up, where John was frustrated with it because it essentially duplicated a proof technique in one of his papers. I believe him that it’s implicit in the work, but honestly, it’s buried deep in the paper, and unless you dug into the details you would not realize it had the implication that QW’s paper highlighted (and which I thought was quite interesting).
Fast-forward to when John and I are thinking about some other research problem.4: For the year, I decided I wanted to work on cute problems, because I was burned out on hard problems. I don’t get much joy out of doing something hard: when you solve a hard problem, everybody thinks you’re soo smart, you get many ivory tower points, and nobody reads the proofs you worked so hard to write. I realize that the necessary component is a strengthening of this idea in the QW paper. I ask John, is this possible? He thinks about it and says, yeah, for sure. (This is what we later term the random purification channel.) This observation is not as easy to make as it might appear: there was folk wisdom, backed by a sizable literature, that something like the RPC could not be possible. And you do not want to bet against a physicist’s intuition. The reason I thought to make this particular strengthening is because we had needed exactly a strengthening of this nature twice, immediately prior to this discussion. (This type of strengthening is what we later term the acorn trick.5: The acorn trick refers to the broader design pattern, but this hasn’t caught on at all. It’s too clever; I am bad at naming things.) This doesn’t happen so often: typically, your first solution is ugly and meandering, and only with a decade of hindsight can you find the clean path forward, the one which feels textbook. Finding the random purification channel felt as natural as playing a puzzle game: you discover a trick, and it somehow is the right way to surmount every barrier in front of you. The trick builds in complexity until you find yourself somewhere completely new.
A little while after, John messages me “oh man i had a genius thought about our project”. There he tells me the reduction from mixed state tomography to pure state tomography. In short, this takes something very hard (mixed state tomography) and reduces it to something very easy (pure state tomography). This is the key thing that kicks off all of the downstream work: shockingly, no one knew of such a reduction prior.6: Despite my terrible memory, I can recall all of these events in great detail. I think the QW discussion was when walking back from La Note in Berkeley. Part of the acorn trick was done in frantic messages to John under the Manhattan bridge, on that fuck ass pier hidden behind construction, while I was supposed to be on vacation. The random purification channel I think was done at my hotel room, on the 4th of July, right before or right after a shower. The John message happened at Outta Sight Pizza in SF; I apologized several times for being distracted by my phone. Research sticks in my head like nothing else. I wish I remembered conversations with people the way I remembered facts about quantum computers.
The real novelty of the RPC is to think about an existing and standard calculation within a proof, and realize that this implies something much stronger than one might expect. My opinion is that this strengthening is the critical insight, and because we did it, we deserve a lot of the credit for it. But I recognize the allure of the contrarian opinion, the thrill of breaking the hype and elevating an underappreciated prior work. You could say:
- In some sense, the random purification channel is a reformulation of QW’s result.
- And in some sense, QW’s result is a more general, better-sold reformulation of John’s paper.
- And yet, all of this uses the techniques first described in the early work of AH. If you look at that work, you can find some suspiciously RPC-shaped results there, but nothing which quite matches.
- And perhaps we were simply at the right place at the right time. We knew a group who was working getting this exact sort of result; and we only learned after that a cryptography paper had beat us to the punch, giving an approximate version of the RPC which was posted to arXiv two days before our paper. More people were thinking about this topic in this particular way, due to recent research developments by popularizations of MZ’s techniques by FM. I think back to a conversation about MZ from after we told him about our idea: he said “these sorts of things tend to be true”. He had the correct intuition before we did: he just didn’t apply it to this particular use case.
And indeed, after the release of our papers, QW and his collaborators have worked to establish their place in the narrative. They stubbornly use their perspectives and language when doing follow-up work to us, and cite back to their own work (and not John’s work) as the originator of the central ideas. Meanwhile, European and Japanese groups have been pushing out papers on RPC like their lives depend on it. These papers use their own language, and the European group in particular is clearly angling to be the definitive source to learn about the RPC. Someone from the European group asked a collaborator of mine if he thought we came up with RPC. Another person from MIT thinks that it really came from AH.
All this has me sympathizing with Perelman.7: I recognize that with the title I am implicitly calling my work a “breakthrough”, and now I have compared myself to Perelman. Please believe me that I am analogizing to landmark math results purely for expository convenience. Well, maybe not that much: leaving academia because other mathematicians are trying to claim credit for your work is petulant and pathetic, especially when you are the most celebrated mathematician in the world. It’s a choice made from ego and misanthropy and self-loathing, or at least that’s how I understand it. Well, I do get that. But mainly, I get that fighting for credit is not pleasant. And unfortunately, I don’t think there’s ever a solid answer to who deserves the credit for a nice result: the answer is dictated by who can sway the research community, and which name will appear in the citations, the wikipedia pages, the mouths of graduate students. It’s as much of a status game as the rest of society, and, though I have the status to still “win” without doing anything, it’s unpleasant to produce a result you’re extremely proud of, only to have it turned into grist for a paper mill which will try to emphasize their own contribution and downplay yours as much as is culturally acceptable.
For better or worse, I do research for selfish reasons. I want credit for the work I do, and I don’t like when that credit is called into question. Simultaneously, I find myself at the helm of the academic prestige allocator, able to withhold credit at will. It’s a brutal machine, and I don’t really blame those who use underhanded or anti-social tactics to get ahead (nor do I blame those who call out that kind of behavior). It’s not so easy to eliminate it: the best thing to do is find people who you trust and respect, and crack jokes with them when someone from across the globe raises your hackles.