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A pure quantum state is a state that can not be written as a probabilistic mixture, or convex combination, of other quantum states. [5] There are several equivalent characterizations of pure states in the language of density operators. [9]: 73 A density operator represents a pure state if and only if:
The macroscopic quantum coherence (off-diagonal long-range order, ODLRO) [25] [26] for superfluidity, and laser light, is related to first-order (1-body) coherence/ODLRO, while superconductivity is related to second-order coherence/ODLRO. (For fermions, such as electrons, only even orders of coherence/ODLRO are possible.)
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.
In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n -th order coherence (for any positive integer n >1) extends the concept of coherence to quantum optics and coincidence ...
However, for measurements correlating detections at multiple detectors, higher-order coherence is involved (e.g., intensity correlations, second order coherence, at two detectors). Glauber's definition of quantum coherence involves nth-order correlation functions (n-th order coherence) for all n. The perfect coherent state has all n-orders of ...
The most general theoretical formalism for Bose–Einstein correlations in subnuclear physics is the quantum statistical approach, [10] [11] based on the classical current [12] and coherent state, [13] [14] formalism: it includes quantum coherence, correlation lengths and correlation times.
Bohr offered an interpretation that is independent of a subjective observer, or measurement, or collapse; instead, an "irreversible" or effectively irreversible process causes the decay of quantum coherence which imparts the classical behavior of "observation" or "measurement". [29] [30] [31] [32]
The idea has been expanded upon by Lee Smolin [7] and Louis Crane, [8] who have both applied the concept to quantum cosmology, and the interpretation has been applied to the EPR paradox, revealing not only a peaceful co-existence between quantum mechanics and special relativity, but a formal indication of a completely local character to reality.