A New Quantum Paradox
By Anil Ananthaswamy,
Quanta, December 2018
Edited by Andy Ross
A new thought experiment is shaking the foundations of quantum physics. The experiment, designed by Daniela Frauchiger and Renato Renner, involves
assumptions that seem reasonable. But it leads to contradictions, so at least one of the assumptions is wrong.
The Frauchiger−Renner experiment has four agents: Alice and her friend Carol, and Bob and his friend Derek. Carol is inside a lab making
measurements on a quantum system, and Alice is outside, monitoring both the lab and her friend. Derek is similarly inside another lab, and Bob
is observing his friend and the lab, treating them both as one system.
Inside the first lab, Carol makes a measurement that shows IN 1/3 of the time and OUT 2/3 of the time. If it is IN, Carol prepares a particle with
spin DOWN, but if OUT, she prepares the particle in a superposition of equal parts UP and DOWN.
Carol sends the particle to Derek, who measures the spin of the particle. Based on the result, Derek can sometimes say what Carol measured. If he
finds the particle spin to be UP, he knows she measured OUT.
Next, Alice measures the state of her friend and her lab, treating all of it as one system, and uses quantum theory to make predictions. Bob does
the same with his friend and lab. First assumption: Quantum theory is universal.
Alice treats her friend and the lab as one system and makes a measurement that puts the system into a superposition of YES or NO. Carol has
already seen IN or OUT. But then Alice puts the lab, Carol included, into a superposition of having seen IN and OUT.
Alice measures the lab system. Say she gets YES for an answer. She can deduce that Derek must have seen spin UP, and therefore that Carol saw OUT.
Second assumption: The predictions made by different agents using quantum theory are not contradictory.
Meanwhile, Bob can make a similar measurement on his friend and his lab, placing them in a quantum superposition. The answer can again be YES or
NO. If Bob gets YES, the measurement lets him conclude that Carol must have seen IN.
Alice and Bob can make measurements and compare their assertions. When Alice gets a YES for her measurement, she infers OUT, and when Bob gets a
YES for his measurement, he infers IN. Most of the time, Alice and Bob will get opposite answers. But in 1/12 of the cases, both Alice and
Bob will get a YES in the same run of the experiment, causing them to disagree on IN or OUT. Third assumption: If an agent measures IN,
another agent cannot measure OUT. Both cannot be right.
Frauchiger and Renner say one of the three assumptions behind the thought experiment must be incorrect.
AR See also blog 2018-09-19.