Quantum generalizations of Bell's inequality

Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail.     

Quantum string representation for Yang-Mills fields

A new way to describe the dynamics of Yang-Mills fields is proposed. The quantum strings with internal degrees of freedom are the principle objects here. A hamiltonian of the system has been obtained in a single string sector. The consideration has been carried out for the SU(2) gauge group.     

Preparation-limited predictions in Einstein-Podolsky-Rosen experiments

It is shown that unavoidable uncertainties arising from the experimental conditions in which systems are prepared for Einstein-Podolsky-Rosen experiments severely limit the possibilities for prediction. In the example originally proposed by EPR, time measurements are necessary for precise position predictions. If the preparation is designed to make the timing errors negligible, the parameters chosen for the preparation fix minimum uncertainties in the predictions leaving the observer no choice in the matter. In the case of correlated spin measurements, the preparation leaves the observer no control over the effect of the detector on the particles; the uncertainty of the previous condition of any one particle is so large that no (classical) prediction of the response of another detector is possible. Thus, there are as yet no proposed experiments which satisfy the conditions required by EPR—i.e., precise predictions which violate the uncertainty principle.     

Quantum-mechanical predictions for EPR experiments with retardation plates

The quantum-mechanical detection probabilities for optical photon pairs are calculated for an EPR experimental arrangement with two plates (one per observer), with arbitrary wave retardations and fast-axis orientations, and two polarizers (one per observer) with arbitrary trasmission-axis orientations. Possible experimental tests of these predictions are suggested.1. It is important to observe that Clauser in his work [19] claimed that the experimental result _exp = –0.015 ± 0.025 was in agreement within errors, with the quantum theoretical prediction _QM = 0.002 of the Freedman's form of the strong Bell's inequality 0. The latter is however incompatible with the quoted values of retardations reported by Clauser that, on the contrary, give the following quantum mechanical prediction: _QM = 0.024, which is hardly compatible with the above experimental result.2. The fast-axes orientations of any inserted quarter-wave plates must remain the same during all the experimental meausrements.     

Quantum communication between N partners and Bell's inequalities

We consider a family of quantum communication protocols involving N partners. We demonstrate the existence of a link between the security of these protocols against individual attacks by the eavesdropper, and the violation of some Bell's inequalities, generalizing the link that was noticed some years ago for two-partners quantum cryptography. The arguments are independent of the local hidden variable debate.     

Quantum correlations and tomographic representation

We review the probabilistic representation of quantum mechanics within which states are described by the probability distribution rather than by the wavefunction and density matrix. Uncertainty relations have been obtained in the form of integral inequalities containing measurable optical tomograms of quantum states. Formulas for the transition probabilities and purity parameter have been derived in terms of the tomographic probability distributions. Inequalities for Shannon and Rényi entropies associated with quantum tomograms have been obtained. A scheme of the star product of tomograms has been developed.     

量子力学混合态表象

在以往的文献中量子力学的表象都是纯态表象,在本文中我们从算符的合理排序和概率统计的正态分布思想出发,首次提出了量子力学混合态表象的概念,并证明了其完备性和正交性.量子力学混合态表象的优点是可以反映算符的多种表示以及其相应的排序规则.     

Quantum chaos in the Wigner representation

The dynamics of a familiar model of stochastic behavior-the quantum kicked rotator-is analyzed in the Wigner representation. Exact nonlocal maps defined on a discrete phase space are derived. The basic dynamics of a quantum kicked rotator can be described satisfactorily by means of a simplified map that incorporates only the discrete nature of the phase space.     

Quantum superspace representation of superconformal algebras

The action for a supersymmetrical point particle introduced in a recent analysis of superspace is shown to have superconformal symmetry when all dimensional parameters are set equal to zero. This fact enables us to construct explicit representations of the d = 3 superconformal groups OSp(N;4) and the d = 4 ones SU(N; 2,2) in both classical and quantum superspace.