Detection Loophole in Bell Tests: Post-Selection with Outcome-Dependent Efficiencies

Sammanfattning

As children, many of us imagined our toys coming to life the moment we looked away, just like in Toy Story. Maybe they walked across the room and secretly planned adventures behind our backs. Surprisingly, physicists ask a very similar question about quantum particles: do they have definite properties before we measure them, or is reality decided at the moment of observation? Understanding the answer has led to technologies such as quantum computing, quantum teleportation, and quantum cryptography. In the quantum world, where particles such as electrons and positrons live, objects do not have definite positions or states but can exist in a superposition of possible states. Even stranger, two particles can become entangled, meaning measuring one, instantly predicts information about measuring the other, no matter how far apart they are. If our particles were Toy Story characters, Woody and Buzz, we could simply ask them questions in a courtroom trial and reveal the secret. In quantum mechanics, these questions are essentially measurements. However, Woody and Buzz can cheat in the trial, and so can our particles, by preplanning the outcome of any measurement in advance. This idea is known as a local hidden-variable theory, and for a long time, it was thought that there was no way to distinguish between such preplanned outcomes and outcomes determined only at the moment of measurement. In 1964, John Bell proposed a test, known as the Bell test, which can reveal this fact. This test can expose any hidden planned strategy. No matter how cleverly our particles coordinate, Bell’s test gives them no easy way to fake the results. His method is a statistical comparison between the results of measurements performed on a pair of particles, which consists of some inequalities that are satisfied if particles have pre-determined outcomes before they are separated, and violated for some of the quantum cases where particles live in a superposition of outcomes, and their outcomes are correlated to each other. But there is still a loophole. Remember the courtroom trial? Now imagine Woody and Buzz invoking the Fifth Amendment and refusing to answer questions. In physical terms, this means that the measurements are inefficient and detectors sometimes fail to produce a result. That missing information can mislead us if we perform our analysis based on the detected particles, a procedure known as post-selection, and this loophole is commonly referred to as the detection loophole. Many efforts have been made to close this loophole, both by increasing the detection efficiency of the detectors and by finding settings in which the minimum efficiency required for a reliable result is lower. In this thesis, we further investigated this loophole under the post-selection assumption. We considered a model in which the efficiency of each measurement depends on its outcome. We then studied how the Bell tests behave when the underlying theory of reality is either a local hidden-variable theory or a quantum-mechanical theory.