The rewindable friend
If a friend's measurement can be perfectly undone, was her result ever a fact?
Known, reproduced
A friend sits in a sealed lab. She measures a qubit and stores the answer in a small quantum memory. Outside, Wigner (here called Alice) has two choices. She can ask the friend what she saw, or she can run the friend's whole lab backwards, which wipes the memory, and then measure the qubit a different way.
The qubit is half of an entangled pair shared with Bob in a second lab. Local Friendliness is the assumption that the friend's result is a real fact and that choices are free and local. Under it, a CHSH-style score (a standard test that adds up four correlations) can never pass 2. A perfect rewind reaches 2.83.
Play the game
starting…
Each trial: Alice and Bob pick settings at random. The friend measures her half of the pair and copies the result into all n memory qubits. While the lab is closed, the environment glimpses each memory qubit with odds g = 10% (a demo choice). Then Alice either asks (she reads the record) or rewinds (she undoes the copying and measures across). Outcomes are drawn from the exact quantum odds: any glimpse leaves the result on record outside, so a rewind after a glimpse gives Alice a coin flip. Right · running score on a log trial axis. Clay: the Local Friendliness bound 2. Moss: perfect rewind 2.83. Brass: this model's exact value √2·(1 + (1 − g)n).
In plain words
If the friend's result were a permanent fact, a rewind could not erase it, and the score would be stuck at 2 or below. Passing 2 says her result was not a fact for everyone. That only works while nothing outside the lab has seen her memory.
Every glimpse of a memory qubit puts the result on record outside, and then the rewind no longer brings back the qubit. The odds that no glimpse lands shrink with every extra memory qubit. So the lab gets a roughly fixed total leak budget, and a bigger mind has to spread it over more parts. Slide n up in the panel and watch the score sink under 2 at fixed glimpse odds. A bigger mind needs a tighter seal.
Prior artKnown. Zeng, Labib and Russo (arXiv 2409.15302) give violation × (1 − p)n ≥ 0.707, found in the notebook's lit check.
Next clickIs the budget counted in bits leaked, or in glimpses?
- The panel uses a simpler memory than the real run. Here the friend copies her result into every memory qubit and does not scramble it, and a glimpse is a full look at one qubit. Its leak budget (shown live in the readout) runs from about 0.6 glimpses for one memory qubit to about 0.85 for twelve, a bit looser than the real run's 0.54–0.68.
- The glimpse odds of 10% per qubit are a demo choice, not a measured number.
- In the real run the friend's "thinking" is a random scramble, not cognition. Leaks are one simple kind of glimpse. Only Alice's friend leaks; Bob's side is ideal, so two-sided noise would be harsher.
- The real run lives in coherence-lab on the lab machine. Its numbers here are taken from the Three Rooms page and were not rerun for this explainer.