On measurement in general quantum theory

1974 ◽  
Vol 21 (2) ◽  
pp. 233-257 ◽  
Author(s):  
B. d’Espagnat
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Yi-You Nie

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries. We deduce the general Schrȍdinger equation of any n particles, and the wave function not only has particle properties of the square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave-particle duality of any n microscopic particles is solved. This paper displays the classical locality and quantum non-locality for any n particle system, shows entanglement origins, and discovers not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, the three kinds of entanglements directly gives lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics is a generalization ( mechanics ) theory of the square root ( of density function ) of classical statistical mechanics. Thus, all current studies on various entanglements and their uses to quantum computer, quantum communications and so on must be further updated and classified by the three kinds of entanglements. Finally, this papers and our previous paper together solve the crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.


1990 ◽  
Vol 05 (27) ◽  
pp. 2231-2239 ◽  
Author(s):  
PETER ORLAND

The general quantum theory of nonrelativistic, infinitely long straight strings of one flavor interacting via a three-body infinitesimal range potential is considered in (2 + 1) dimensions. It is proved that the tetrahedron equation of Zamolodchikov is satisfied only when the potential is either zero or infinitely repulsive. Therefore the Bethe ansatz is valid only for these special cases.


Author(s):  
Arthur I. Fine

We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.


2009 ◽  
Vol 16 (01) ◽  
pp. 29-48 ◽  
Author(s):  
Francesco Buscemi ◽  
Michał Horodecki

We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys. Rev. Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent approaches adopted in order to derive information-disturbance tradeoffs in quantum theory. We focus in particular on those tradeoffs, constituting the vast majority of the literature on the subject, where disturbance is defined either in terms of average output fidelity or of entanglement fidelity.


2020 ◽  
pp. 1-1
Author(s):  
Ben Campbell Bieżanek ◽  

2014 ◽  
Vol 23 (05) ◽  
pp. 1450052 ◽  
Author(s):  
Edward Anderson ◽  
Sophie Kneller

We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.


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