whereZ,Xare the standard 2×2 Pauli matrices. The numerator in Eq. (7.33)
takes the form
(^1) M/ 2 ⊗
(
12 ⊗ 12 +aZ⊗Z+ 12 ⊗bX)
⊗ (^1) M/ 2 (7.36)
The brackets can be written as:
| 0 〉〈 0 |⊗( 1 +aZ+bX) +| 1 〉〈 1 |⊗( 1 −aZ+bX) (7.37)
( 1 ±aZ+bX) ≥ 0 when a^2 +b^2 ≤ 1, and the resulting expression forρ is
manifestly separable. Rescaling the coordinates gives the radiusr 0 for the Clifford
ball of separable state.
Acknowledgement
The research has been supported by ISF. We thank Yuval Lemberg for help in the
initial stages of this work and Andrzej Kossakowski for his encouragement.