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The Kiss Notation

I am attending a course in Quantum Information Processing. As with Quantum Mechanics, Quantum Information Processing uses the Dirac’s notation (Defined Below).

Dirac’s Noation:

  1. |\psi\rangle represents a column vector – is called ‘ket psi’.
  2. \langle\psi| represents the conjugate transpose of |\psi\rangle – is called ‘bra psi’.

In quantum computation one often comes across the following notation

|\psi\rangle\langle\phi|

Instead of pronouncing the above notation as ‘bra psi ket phi'(which is rather lenghty to pronouce) – we would say it as ‘psi kiss phi’.

The speciality of the kiss notation is that if you take a dagger of the kiss notation, i.e. (|\psi\rangle\langle\phi|)^\dagger, it still remains kiss, with the psi and phi chaging there position. (Re-enforcing our idea of that fact that love cannot be killed :-D)

(|\psi\rangle\langle\phi|)^\dagger = |\phi\rangle\langle\psi|

The new LATEX commands for the above formulation are:

  1. \newcommand*{\kiss}[2]{|#1 \rangle\langle #2|}
  2. \newcommand*{\kisso[1]{|#1 \rangle\langle #1|}

The above commands can be updated in the LATEX Preamble of LYX or can be written in the begining of the TEX document and can be used in the document.

Usage of the above commands are as follows:

  1. \kiss{i}{u} will have the following ouput – |i\rangle\langle u|
  2. \kisso{i} will have the following output – |i\rangle\langle i|