Conventions and formulas

Section author: Nicolás Quesada <>, Ville Bergholm, Josh Izaac

“The nice thing about standards is that you have so many to choose from.” - Tanenbaum [58]

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.


In Strawberry Fields we use the convention \(\hbar=2\) by default, but other conventions can also be chosen on engine initialization. In this document we keep \(\hbar\) explicit.


More information about the definitions included on this page are available in [59] and [60].

The Kraus representation of the loss channel is found in [61] 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 [62] Eq. A.4.3 of Appendix A.