# Engineering Quantum States of Light

In my talk I will introduce a notion of a linear-optical quantum state generator (LOQSG). This is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and post-selection using photon counters. I show that the LOQSG can be concisely described in terms of the language of algebraic geometry.

I illustrate the power of this language by applying the Groebner-basis technique to solve problem of how to construct a general LOQSG analytically. In particular, I disprove a

conjecture concerning the preparation of a maximally path-entangled ”NOON”

state by providing a counterexample, using these methods and draw a new upper bound on the resources required for NOON-state generation.