The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.     

Quantum mechanics and the local observer

A notion of local observer inspired by the work of Segal is introduced here in the Hilbert space theory of quantum mechanics. The local observer finds a mathematical place in the Hilbert space through local negation or complementation. A logicomathematical theory of local negation is presented and its implications for quantum logic and the problem of measurement are discussed. The setting is constructivist mathematics and the main result of the paper states that the introduction of a local observer implies the nonorthocomplementability of the whole Hilbert space even in the finite-dimensional case. Making a mathematical place for the observer (the “projector”) thus modifies the structure of the observables or the system of the projections, in accordance with a nonclassical theory of quantum-mechanical measurement.     

Cramér-Rao inequalities for operator-valued measures in quantum mechanics

The theory of estimation of parameters of quantum-mechanical density operators is expressed in terms of the measurement of operator-valued measures. Lower bounds on mean-square errors of parameter estimates are set by two quantum-mechanical forms of the Cramér-Rao inequality of classical statistics, derived here in terms of such measures. The results are exemplified by the simultaneous estimation of the real and imaginary parts of the complex amplitude of a coherent oscillation in the presence of thermal noise.This research was supported by grant NSF GK-33811 from the National Science Foundation.     

On the theory of the spontaneous magnetization of thin films. Part I

Conclusion From (3) it is seen that the quantum-mechanical theory of thin films leads to quite analogous results as for massive specimens. It is obvious that we should arrive at the same results as in (3) if from the very beginning we solved the whole problem by means of the theory of molecular fields putting the molecular fields of the individual atomic planes proportional to their magnetization. We shall therefore make use of this fact in the future by working with the method of molecular fields which permits of a somewhat more flexible procedure than the quantum-mechanical solution. At the same time, however, there appear in the equations constants of the molecular fields which are not more closely defined and which, as we know, are proportional to the exchange interaction energy between neighbours but with the present state of the theory this is not a disadvantage in comparison with the quantum-mechanical procedure, since the exchange integrals have not yet been calculated.A comparison of (3) with experiment will be left to the second part of this paper, where we shall compare the results of measurement with the equivalent equations in the molecular-field form.This paper was read at the international conference on magnetic phenomena in Moscow, 1956.     

Measurement of the photon statistics and the noise figure of a fiber-optic parametric amplifier

We report measurement of the noise statistics of spontaneous parametric fluorescence in a fiber parametric amplifier with single-mode, single-photon resolution. We employ optical homodyne tomography for this purpose, which also provides a self-calibrating measurement of the noise figure of the amplifier. The measured photon statistics agree with quantum-mechanical predictions, and the amplifier's noise figure is found to be almost quantum limited.     

Covariant collapse of the state vector and realism

We point out that the assumption that a quantum-mechanical state vector collapses in a Lorentz-covariant way upon measurement is consistent, but that it implies that the state vector, and any reality which it represents, depends on position. We consider the specific example of collapse along the forward light cone of the measurement.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

Photodetachment cross section of S^- in electric and magnetic fields＊

In this paper, the quantum-mechanical photodetachment cross section of S^- in uniform electric and magnetic fields at arbitrary angles is presented. It compares the quantum-mechanical cross section with the quantum source formalism cross section. The results show that at large angle, the two results have good agreements, however, with the decrease of the angles, they deviate obviously from each other. The reasons for this discrepancy are also discussed.     

Uncertainty measures and uncertainty relations for angle observables

Uncertainty measures must not depend on the choice of origin of the measurement scale; it is therefore argued that quantum-mechanical uncertainty relations, too, should remain invariant under changes of origin. These points have often been neglected in dealing with angle observables. Known measures of location and uncertainty for angles are surveyed. The angle variance angv {ø} is defined and discussed. It is particularly suited to the needs of quantum theory, because of its affinity to the Hilbert space metric, and its use of the basic sine and cosine operators. Corresponding uncertainty relations involving azimuthal or phase angles are indicated, and their relevance to study and definition of coherent states is briefly reviewed.     

A note on the Lüders-Von Neuman formula of collapse

The collapse in a quantum-mechanical measurement is treated as a physical process, described by a superoperator mapping states into states and depending only on the measured observable. The assumption that the states with a sharp value of the measured observable remains unchanged yields the Lüders-Von Neuman formula.     

Neutron phase imaging and tomography

We report how a setup consisting of three gratings yields quantitative two- and three-dimensional images depicting the quantum-mechanical phase shifts of neutron de Broglie wave packets induced by the influence of macroscopic objects. Since our approach requires only a little spatial and chromatic coherence it provides a more than 2 orders of magnitude higher efficiency than existing techniques. This dramatically reduces the required measurement time for computed phase tomography and opens up the way for three-dimensional investigations of previously inaccessible quantum-mechanical phase interactions of neutrons with matter.     

Can dynamic neutron scattering help to understand a thermodynamic variant of an internal quantum-mechanical experiment in the angstrom range?

A chain of ideas is described connecting the theory of quantum-mechanical experiments with practical research in the relaxation of liquids, biological materials, and materials science. The chain culminates at the proposal of an experimentum crucis comparing dynamic neutron scattering, dynamic calorimetry, and computer simulation of the same substances at the crossover region of the dynamic glass transition. The conclusiveness of the experimentum crucis backwards the chain is discussed. The role of relaxation of liquids in confining geometries is also discussed, especially with respect to the confirmation of the von Laue variant for the characteristic length of glass transition as alternative to their Gibbs treatment that results in too large lengths.Received: 1 January 2003, Published online: 14 October 2003PACS: 03.65.Ta Foundations of quantum mechanics; measurement theory - 64.70.Pf Glass transitions - 61.12.-q Neutron diffraction and scattering     

A proposal for a model of many-successive measuring process

A quantum-mechanical model of a detector monitoring the decay of an unstable object is constructed. Detailed investigation of the time evolution of this model shows that under some conditions the non-decay probability of many successively measured unstable particles coincides with that following from the state-reduction postulate. The probability of realizing continuous measurement without the Zenoparadox is demonstrated for this model.     

A note on relative entropy

The quantum-mechanical concept of relative entropy is discussed from an information-theoretic point of view. We show that not all definitions found in the recent literature are equally suitable for the purpose of statistical inference by entropy maximization.