arXiv subjects
Publications and source records attributed to G. Mahoux.
An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.
We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $ρ(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $ρ(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $ρ(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.
For the eigenvalues of $p$ complex hermitian $n\times n$ matrices coupled in a chain, we give a method of calculating the spacing functions. This is a generalization of the one matrix case which has been known for a long time.