How to construct a non-trivial POVM measurement example?

How to construct a non-trivial POVM measurement example?

How to construct a non-trivial (non-projective) POVM measurement example? But this is simply a projective measurement (on state Ψ ). How to construct a non-trivial (non-projective) POVM measurement example?

How are POVM measurements on a single qubit physically realizable?

In Nielsen and Chuang Quantum Computation and Quantum Information book section 2.2.6, a POVM of three elements are used to measure a single qubit in order to know for sure whether the state is | 0 ⟩ or | + ⟩ if the first two measurement results are obtained, and do not infer the state when the third result is obtained.

How does the POVM work in Nielsen and Chuang?

This is the way that Nielsen and Chuang’s POVM works. You either learn | 0 ⟩, | + ⟩, or a third outcome (call it “6”) that doesn’t tell you anything about the qubit. Thanks Peter for the clarification about information vs. outcomes.

How is the POVM element related to the state?

Quantum properties of measurements. The measurement is projective when its pre-measurement state is a pure quantum state . Thus, the corresponding POVM element is given by: where is in fact the detection efficiency of the state , since Born’s rule leads to . Therefore, the measurement can be projective but non-ideal,…

Why do we need mixed states in POVM?

Mixed states are needed to specify the state of a subsystem of a larger system (see purification of quantum state ); analogously, POVMs are necessary to describe the effect on a subsystem of a projective measurement performed on a larger system.

Which is the most general formulation of a POVM?

(November 2018) In functional analysis and quantum measurement theory, a positive-operator valued measure (POVM) is a measure whose values are non-negative self-adjoint operators on a Hilbert space, and whose integral is the identity operator. It is the most general formulation of measurements in quantum physics.