Conventions and formulas

Section author: Nicolás Quesada <nicolas@xanadu.ai>, Ville Bergholm, Josh Izaac


“The nice thing about standards is that you have so many to choose from.” - Tanenbaum [65]

In this section, we provide the definitions of various quantum operations used by Strawberry Fields, as well as introduce specific conventions chosen. We’ll also provide some more technical details relating to the various operations.

Note

In Strawberry Fields we use the convention \(\hbar=2\) by default, but other conventions can also be chosen by setting the global variable strawberryfields.hbar at the beginning of a session. In this document we keep \(\hbar\) explicit.

Note

More information about the definitions included on this page are available in [66] and [67].

The Kraus representation of the loss channel is found in [68] Eq. 1.4, which is related to the parametrization used here by taking \(1-\gamma = T\).

The explicit expression for the harmonic oscillator wave functions can be found in [69] Eq. A.4.3 of Appendix A.