Annotated Bibliography: Leoński’s Quantum Scissors — finite dimensional states engineering

W. Leoński, A. Kowalewska-Kudłaszyk, Chapter 3 – Quantum Scissors – Finite-Dimensional States Engineering, In: Emil Wolf, Editor(s), Progress in Optics, Elsevier, 2011, Volume 56, Pages 131-185. (Mickiewicz University, Poland)

Type: Book Chapter

Summary: They discuss methods of generating finite dimensional Fock-basis state from infinite-dimensional space and truncation. They describe coherent states (finite and infinite), squeezed state, and entangled state on Fock basis, as they use these states to generate a general state later. They go on to describe the method of generating truncated states using quantum scissors.

Linear quantum scissors (LQS) methods use the beam splitters as their main component in creating a general state of N photon. The state is controlled in part by the input state. One of the method uses Mach-Zehnder interferometer as the setup. The state is mostly post-selected with the exception of the BS-array scheme.

Nonlinear quantum scissors (NQS) methods involve Kerr medium inside high-Q cavity or Mach-Zehnder interferometer, fed by coherent and vacuum state. The state is post-selected. In this case, the photons are generated by the nonlinear medium and therefore cannot reach high number Fock state. The most shown in the paper is \left|2\right\rangle.

This work also include discussions on limitation and imperfection of the schemes of LQS and its connection to quantum teleportation.

Comments: This chapter is a review of the existing proposed techniques. Some of these techniques must have been implemented, but it is not clear which nor that seems to be the focus of the work.

From the perspective of quantum-enhanced metrology, NQS is not a very useful technique because the probability of getting high Fock states get progressively smaller because of the weak nonlinear interaction. LQS is more the way to go. although the input state requires might still be unrealistic (high number Fock state, for example).


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