Quantum Information Processing, Vol. 6, No. 1, February 2007 (© 2006)
Mathematical Theory of the Duality Computer
in the Density Matrix Formalism
Gui Lu Long
Received May 8, 2006; accepted July 3, 2006; Published online November 30, 2006
We give the mathematical theory of duality computer in the density matrix for-
malism. This result complements the mathematical theory of duality computer of
Gudder in the pure state formalism.
KEY WORDS: Duality computer; quantum wave divider; quantum wave com-
binor; density matrix; partial wave function measurement.
PACS: 03.67.Hk; 03.65.Ud; 03.67.Dd; 03.67.-a.
Very recently, Gudder has given the mathematical theory for the duality
In his timely work, he has provided two descriptions, one is
in the pure state formalism and the other is in the mixed state formal-
ism for the mathematics of duality computer. The duality computer is a
new type of computing machine based on the general principle of quan-
tum interference proposed in Ref. 2. Notably, unsorted database search
problem may be solved by using only a single query, and all NP-complete
problems may have polynomial algorithms in the duality computer.
In Ref. 1, it has been pointed out that a paradoxical situation occurs
with the mixed state situation where the formalism gives a different result
from the pure state formalism, and in particular, the advantage of duality
computer was lost in the mixed state formalism.
In this paper, we give the mathematical theory of the duality computer in
the density matrix formalism. This density matrix formalism description is in
Key Laboratory for Quantum Information and Measurements and Department of Physics,
Tsinghua University, Beijing 100086, China.
Key Laboratory of Atomic and Molecular NanoSciences, Tsinghua University, Beijing
100084, China. E-mail: email@example.com
1570-0755/07/0200-0049/0 © 2006 Springer Science+Business Media, Inc.