Realization of positive-operator-valued measures by projective measurements without introducing ancillary dimensions

Realization of generalized quantum measurements, or positive-operator-valued measures (POVMs), is a fundamental problem in quantum mechanics and quantum information science. Many tasks, such as quantum state discrimination and entanglement transformation, require nonorthogonal measurements to success or to achieve the optimal efficiency. During recent years much effort has been devoted to the implementation of POVMs on various kinds of physical systems [1]. Many of the proposed schemes are derived from Neumark’s theorem [2], which asserts that any POVM can be realized by extending the original Hilbert space to a larger space and performing a projective measurement on the extended space. In spite of its universality, this method has the drawback of needing a collective operation on the original system and an ancillary system, which may be difficult to implement in practice.