Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Canonical Decompositions of n-qubit Quantum Computations and Concurrence



Stephen Bullock, G K. Brennen


The two-qubit canonical decomposition SU(4) = [SU(2) SU(2)]?[SU(2) SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the n-tangle |*| (-i? ) ¿ (-i? ) |?>|2 for n even. Thus, the C.C.D. shows that any n-qubit quantum computation is a composition of a computation preserving this generalized tangle, a computation in A which applies relative phases to a set of GHZ states, and a second
Journal of Mathematical Physics


concurrence, entanglement, quantum computation


Bullock, S. and Brennen, G. (2003), Canonical Decompositions of n-qubit Quantum Computations and Concurrence, Journal of Mathematical Physics, [online], (Accessed March 4, 2024)
Created February 25, 2003, Updated February 17, 2017