Physics
Presenter(s): Conner Carnahan
Advisor(s): Dr. Matthew Leifer
Quantum mechanics has remarkable differences for measurements from classical mechanics, and this is a notion of incompatible measurements. Intuitively what it says is that given some system, it is not guaranteed that you will be able to find a way to measure the system in two different ways. The most famous result from this is the Heisenberg uncertainty principle, which states that there is a bound on the uncertainty you can have when you measure the momentum of a particle given the uncertainty you have of its position. My research project has been based on an extension to this concept, which is called Incompatibility Robustness. What is already known in quantum theory is that if I have two measurements I wish to perform on a system, even if I cannot do both of them, I can create a new measurement which is a noisy version of the two I wish to perform. This can be understood as introducing a probability of failure to measure what I want correctly, which will allow me to measure a larger set of properties at the same time. The probability that I don't measure what I want is roughly the Incompatibility Robustness, and is a measure that can be theoretically found for any set of two measurements. This measure is a way to quantitatively study the concept of incompatibility, which we hope to use in the proofs of some general theorems. Specifically, I have derived an explicit formula for a certain set of measurements on a Qubit, and have performed numerical analysis on larger measurements.