Xiao-Ming Lu, Zhe Sun, Xiaoguang Wang, Shunlong Luo, C. H. Oh
It is known that a family of quantum states cannot be broadcast if they are not commutative. We conceive a situation that the object we want to broadcast is the statistical distinguishability about an analog signal encoded in quantum states. Measuring the statistical distinguishability by the quantum Fisher information (QFI), we show that the QFI cannot be cloned, whilst it might be broadcastable even when the input states are non-commutative. Moreover, we identify all the states in which the QFI is broadcast, and give a necessary and sufficient condition for the broadcastability of the QFI when some extraordinary situations are excluded.
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http://arxiv.org/abs/1206.2821
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