On commutativity of quantum weakest preconditions

Details On commutativity of quantum weakest preconditions On commutativity of quantum weakest preconditions

2011-08-23

arxiv.org/abs/1108.4607v4

Computer Science

Logic in Computer Science

Some typos corrected, comments are welcome

Scientific paper

In a recent letter by Ying et al. [Inf. Process. Lett. 104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. However, the sufficient and necessary condition for quantum weakest preconditions remains open. This letter presents a simple characterization of the commutativity of quantum weakest preconditions. We show that, two quantum weakest preconditions $wp(\mathcal{E})(M)$ and $wp(\mathcal{E})(N)$ commute if and only if the product $wp(\mathcal{E})(M)\cdot wp(\mathcal{E})(N)$ (or, $wp(\mathcal{E})(N)\cdot wp(\mathcal{E})(M)$) is Hermitian.

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