Possibility of a minimal purity-measurement scheme critically depends on
the parity of dimension of the quantum system [PDF]
Toru Tanaka, Gen Kimura, Hiromichi Nakazato
In this paper, we propose a minimal model for directly measuring the purity of a quantum state (and the overlap between two quantum states) in a way that the measurement device is minimally composed. With an input of two identical and independent copies of an unknown quantum state, the model is composed of a local yes-no measurement on a single system after a global unitary interaction. We show that the measurability of the purity within this model critically depends on the parity of dimension of the quantum system: the purity measurement is possible for odd dimensional quantum systems, while it is impossible for even dimensional cases.
View original: http://arxiv.org/abs/1209.0079
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