In:
Journal of Mathematical Physics, AIP Publishing, Vol. 46, No. 8 ( 2005-08-01)
Abstract:
The no-cloning theorem says there is no quantum copy machine which can copy any one-qubit state. Inner product preserving was always used to prove the no-cloning of nonorthogonal states. In this paper we show that the no-cloning of nonorthogonal states does not require inner product preserving and discuss the minimal properties which a linear operator possesses to copy two different states at the same device. In this paper, we obtain the following necessary and sufficient condition. For any two different states ∣ψ⟩=a∣0⟩+b∣1⟩ and ∣φ⟩=c∣0⟩+d∣1⟩, assume that a linear operator L can copy them, that is, L(∣ψ,0⟩)=∣ψ,ψ⟩ and L(∣φ,0⟩)=∣φ,φ⟩. Then the two states are orthogonal if and only if L(∣0,0⟩) and L(∣1,0⟩) are unit length states. Thus we only need linearity and that L(∣0,0⟩) and L(∣1,0⟩) are unit length states to prove the no-cloning of nonorthogonal states. It implies that inner product preserving is not necessary for the no-cloning of nonorthogonal states.
Type of Medium:
Online Resource
ISSN:
0022-2488
,
1089-7658
Language:
English
Publisher:
AIP Publishing
Publication Date:
2005
detail.hit.zdb_id:
219135-0
detail.hit.zdb_id:
1472481-9
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