1

I am reading about the Quantum Pigeon Hole Principle and having trouble understanding how the states are measured. Specifically from this paper. From equation (4) through equation (7).

Maxsash
  • 111
  • 2
  • 1
    Not really addressing the titular question, but in terms of understanding that paper you might find this helpful: https://algassert.com/quantum/2016/01/30/quantum-pigeonhole.html – Craig Gidney Jun 05 '21 at 19:10
  • By "how states are measured" do you mean physically, mathematically, or both? Some measurements are represented by a set of projection operators that sum to identity, and each correspond to a different measurement outcome (in turn causing the state to evolve with the measurement update rule). – Quantum Mechanic Jun 05 '21 at 20:45
  • @QuantumMechanic I meant mathematically, specific to the paper I have linked to. I am having trouble understanding the equations used [(4) to (7) in the paper]. And while I know how to calculate the probability of getting a specific state after measurement and how to calculate the post measurement state. I have not been able to understand the reasoning and conclusions of the aforementioned paper. – Maxsash Jun 05 '21 at 21:03
  • @Maxsash so you are asking how measurements are performed specifically in said paper? If so, the current title is a bit misleading. I'd suggest editing it to more closely reflect what you are actually asking – glS Jun 06 '21 at 09:08
  • @glS Yes but if I could get an explanation for the 'capital PI' or 'projection operators' as they are referred to in the paper it would help tremendously and asking this question keeps it more generalized which I thought would be best. I know it can be improved but I don't see how. If you would be kind enough to help out with that I would appreciate it. – Maxsash Jun 06 '21 at 13:06
  • 1
    @Maxsash An (orthogonal) projection is literally a geometric operation and a pretty standard object in linear algebra. Have you checked out Wikipedia? https://en.wikipedia.org/wiki/Projection_(linear_algebra) Or are you having trouble with braket (Dirac) notation? – Markus Heinrich Jun 09 '21 at 09:38

0 Answers0