Abstract
We derive that sufficient and necessary conditions for existence of a quantum channel ϕ and a generalized unitary operation ɛ sending Ai to Bi (1 ⩾ i ⩾ k) for two given families {Ai}i=1k, {Bi}i=1k of matrices, respectively. As an application, a sufficient and necessary condition for existence of a unitary duality quantum computer with given input-output states is obtained.
Highlights
The theory of quantum information and quantum computation [1] is a result of the effort to generalize classical information theory to the quantum world
A quantum system is described by a finite dimensional Hilbert space H, a state of the system is described by a unit vector in H, or a density operator
A convex combination of unitary operators is called a generalized quantum gate [2,3,4], which came from a duality quantum computer [5,6,7,8,9,10,11,12,13,14]
Summary
The theory of quantum information and quantum computation [1] is a result of the effort to generalize classical information theory to the quantum world. (ΠAs ⊗ ΠtB)ρ(ΠAs ⊗ ΠtB) = ρ, s=1 t=1 where ΠAs and ΠtB are one-dimensional orthogonal projections on HA and HB, respectively If such a Π exists, we call the state ρ is classical correlated [17,18,19,20,21,22]. The following question arises naturally: given families {Ai}ki=1 ⊂ MN and {Bi}ki=1 ⊂ MM of matrices, to discuss the existence and construction of a quantum channel c The Author(s) 2012.
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