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Most of my knowledge in the field of Quantum Information comes from the lectures I've had as an MSc Student and from Nielsen and Chuang's textbook. Both of these focused on the "qubit" formalism. By that, I mean:

  • Working in a finite dimensional Hilbert space;
  • Working in a "discrete" Hilbert space (by that I mean that its bases are countable);
  • $|i\rangle$ represents a vector of the canonical basis of the Hilbert space, and more generally a vector $|\psi\rangle$ represents a state the quantum system can be in (focusing on pure states for now).

Now, I've heard that the mathematical formalism is quite different to deal with quantum optics. I would like to learn about it, but I would like to avoid as much as possible the "physics" side of it, since saying that I'm bad at it would be an euphemism.

Are there some resources that teach about this domain while focusing on the mathematical side of things, or that are addressed to those familiar with the qubit formalism?

If it's not clear (because I don't know what I'm talking about), the topic I would like to learn about concerns stuff like:

  • Gaussian states
  • Coherent states
  • Wiener functions (I think that's what they're called? Something with two-dimensional gaussian distributions)
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There are a number of rather well regarded review papers, such as: https://doi.org/10.48550/arXiv.quant-ph/0503237, https://doi.org/10.1016/j.physrep.2007.04.005, https://doi.org/10.1103/RevModPhys.84.621, https://doi.org/10.1142/S1230161214400010.

You might be interested in this recent tutorial https://doi.org/10.1103/PRXQuantum.2.030204.

This one is a self-described quick reference https://doi.org/10.48550/arXiv.2102.05748.

Btw, you are referring to Wigner functions (Wiener processes are a thing in quantum measurement theory but I doubt it's what you're looking for).

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