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In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system.The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable".
In quantum mechanics, PVMs are the mathematical description of projective measurements. [clarification needed] They are generalized by positive operator valued measures (POVMs) in the same sense that a mixed state or density matrix generalizes the notion of a pure state.
POVMs are a generalization of projection-valued measures (PVM) and, correspondingly, quantum measurements described by POVMs are a generalization of quantum measurement described by PVMs (called projective measurements). In rough analogy, a POVM is to a PVM what a mixed state is to a pure state.
The physical significance of the projective Hilbert space is that in quantum theory, the wave functions and represent the same physical state, for any .The Born rule demands that if the system is physical and measurable, its wave function has unit norm, | =, in which case it is called a normalized wave function.
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state.
Quantum tomography is a process by which, given a set of data representing the results of quantum measurements, a density matrix consistent with those measurement results is computed. [ 25 ] [ 26 ] When analyzing a system with many electrons, such as an atom or molecule , an imperfect but useful first approximation is to treat the electrons as ...
In this context, informational completeness is the property of a POVM of allowing to fully reconstruct input states from measurement data. The properties of SIC-POVMs make them an interesting candidate for a "standard quantum measurement", utilized in the study of foundational quantum mechanics, most notably in QBism [citation needed].
The one-way quantum computer, also known as measurement-based quantum computer (MBQC), is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements.