## Algebra of Classical and Quantum Binary Measurements

**Authors:** C A Brannen

The simplest measurements in physics are binary; that is, they have only two possible
results. An example is a beam splitter. One can take the output
of a beam splitter and use it as the input of another beam splitter. The compound measurement
is described by the product of the Hermitian matrices that describe the beam splitters.
In the classical case the Hermitian matrices commute (are diagonal) and the measurements
can be taken in any order. The general quantum situation was described by Julian Schwinger
with what is now known as ``Schwinger's Measurement Algebra''. We simplify his results
by restriction to binary measurements and extend it to include classical as
well as imperfect and thermal beam splitters. We use elementary methods to introduce
advanced subjects such as geometric phase, Berry-Pancharatnam phase, superselection sectors,
symmetries and applications to the identities of the Standard Model fermions.

**Comments:** 22 Pages. Added derivation of complex numbers in QM and minor changes. As submitted to journal.

**Download:** **PDF**

### Submission history

[v1] 2018-01-25 01:08:02

[v2] 2018-01-30 23:57:24

**Unique-IP document downloads:** 63 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*