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Note: An alternate spelling of this is "Neumark's Theorem" Naimark's dilation theorem [4] shows how POVMs can be obtained from PVMs acting on a larger space. This result is of critical importance in quantum mechanics, as it gives a way to physically realize POVM measurements.
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]. SIC-POVMs have several applications in the context of quantum state tomography [ 1 ] and quantum cryptography , [ 2 ] and a possible connection has ...
The old quantum theory is a collection of results from the years 1900–1925 [23] which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. [24] The theory is now understood as a semi-classical approximation [25] to modern quantum mechanics. [26]
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.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
Later, Busch [39] and independently Caves et al. [24]: 116 [40] proved an analogous result for a more general class of measurements, known as positive-operator-valued measures (POVMs). The set of all POVMs includes the set of von Neumann measurements, and so the assumptions of this theorem are significantly stronger than Gleason's.
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This was first demonstrated by Bell through Bell's Theorem, which showed that certain predictions of quantum mechanics are incompatible with the principle of locality (an idea that objects are only directly influenced by their immediate surroundings). [11] If the POVMs on Alice's side are compatible, then they will never lead to Bell ...