Positive operator valued measure in quantum information processing

Abstract

The positive operator valued measure (POVM), also known as the probability operator valued measure, is useful in quantum information processing. The POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and history of POVMs in quantum theory, and an expository discussion of the quantum mechanics of photonic qubits, a particular implementation of a POVM for use in the measurement of photonic qubits is reviewed.