Conventions and formulas

“The nice thing about standards is that you have so many to choose from.” - Tanenbaum [1]

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 by setting the global variable sf.hbar at the beginning of a session. In this document we keep \(\hbar\) explicit.


More information about the definitions included on this page are available in [2] and [3].

The Kraus representation of the loss channel is found in [4] 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 [5] Eq. A.4.3 of Appendix A.



We also provide some details of the quantum photonics terms that are commonly used across Strawberry Fields, when programming and using photonic quantum computers.

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Andrew S. Tanenbaum and David J. Wetherall. Computer networks, 5th Ed. Prentice Hall, 2011.


S.M. Barnett and P.M. Radmore. Methods in Theoretical Quantum Optics. Oxford Series in Optical and Imaging Sciences. Clarendon Press, 2002. ISBN 9780198563617. URL:


Pieter Kok and Brendon W. Lovett. Introduction to Optical Quantum Information Processing. Cambridge University Press, 2010. ISBN 9781139486439. URL:


Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, and Liang Jiang. Performance and structure of bosonic codes. Aug 2017. arXiv:1708.05010.


J J Sakurai. Modern Quantum Mechanics. Addison-Wesley Publishing Company, 1994.