Editing Beam splitter (section)

=== Application for quantum computing ===
In 2000 Knill, Laflamme and Milburn ([[KLM protocol]]) proved that it is possible to create a universal [[quantum computer]] solely with beam splitters, phase shifters, photodetectors and single photon sources. The states that form a qubit in this protocol are the one-photon states of two modes, i.e. the states |01⟩ and |10⟩ in the occupation number representation ([[Fock state]]) of two modes. Using these resources it is possible to implement any single qubit gate and 2-qubit probabilistic gates. The beam splitter is an essential component in this scheme since it is the only one that creates [[Quantum entanglement|entanglement]] between the [[Fock states]].

Similar settings exist for [[continuous-variable quantum information|continuous-variable quantum information processing]]. In fact, it is possible to simulate arbitrary [[Bogoliubov transformation|Gaussian (Bogoliubov) transformations]] of a quantum state of light by means of beam splitters, phase shifters and photodetectors, given [[Squeezed coherent state|two-mode squeezed vacuum states]] are available as a prior resource only (this setting hence shares certain similarities with a Gaussian counterpart of the [[KLM protocol]]).<ref>{{cite journal|last1=Chakhmakhchyan|first1=Levon|last2=Cerf|first2=Nicolas|title= Simulating arbitrary Gaussian circuits with linear optics|journal=Physical Review A|date=2018|volume=98|issue=6 |page=062314|doi=10.1103/PhysRevA.98.062314|arxiv=1803.11534|bibcode=2018PhRvA..98f2314C }}</ref> The building block of this simulation procedure is the fact that a beam splitter is equivalent to a [[Squeezed coherent state#Operator representation|squeezing transformation]] under ''partial'' [[T-symmetry|time reversal]].