by Note that , so when outcome is obtained we are certain that the quantum state is , and when outcome is obtained we are certain that the quantum state is . The probability of having a conclusive outcome is given by when the quantum system is in state or with the same probability. This result is known as the Ivanovic-Dieks-Peres limit, named after the authors who pioneered UQSD research. Using the above construction we can obtain a projective measurement that physically realises this POVM. The square roots of the POVM elements are given by where Labelling the three possible states of the ancilla as , , , and initializing it on the state , we see that the resulting unitary takes the state together with the ancilla to and similarly it takes the state together with the ancilla to A measurement on the ancilla then gives the desired results with the same probabilities as the POVM. This POVM has been used to experimentally distinguish non-orthogonal polarisation states of a photon, using the path degree of freedom as an ancilla. The realisation of the POVM with a projective measurement was slightly different from the one described here. See also SIC-POVM Quantum measurement Mathematical formulation of quantum mechanics Density matrix Quantum operation Projection-valued measure Vector measure References POVMs K. Kraus, States, Effects, and Operations, Lecture Notes in Physics 190, Springer (1983). E.B.Davies, Quantum Theory of Open Systems, Academic Press (1976). A.S. Holevo, Probabilistic and statistical aspects of quantum theory, North-Holland Publ. Cy., Amsterdam (1982). External links Interactive demonstration about quantum state discrimination Quantum information theory Quantum measurement