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Manuscript Title: An inversion of quantum mechanics.
Authors: E. Lubkin, T. Lubkin
Catalogue identifier: ACYP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 16(1979)207
Programming language: Fortran.
Computer: UNIVAC 1106.
Operating system: EXEC 8.
RAM: 20K words
Word size: 36
Peripherals: disc.
Keywords: Quantum correlations, Quantum mechanics, Probability, Quantum model, Mechanics matrix, Quantum model, Quantum effects in Social sciences, Quantum psychology, Density matrix, State and test matrices, Quantum probabilities, Mixed test, Finite spin system, Spin-system density, General purpose, Statistical methods.
Classification: 4.13.

Nature of problem:
The task is to seek quantum correlations in raw probability data. A table of counts or probabilities is input to MATRIXFORMAT or to CLSSCLFORMAT. The first produces a quantum matrix model listing matrices and also trace-formula theoretical output probabilities: the second produces a classical model by being restricted to diagonal matrices. By comparing relative success of these two programs in fitting the data, user attempts to determine whether the data exhibit quantum interference phenomena, i.e., whether the data favor a quantum- mechanical interpretation. Another kind of application is determination of density matrices and test matrices from probability data in an already accepted quantum-mechanical context, without any prior assumption of a dynamical model.

Solution method:
A theory-experiment probability discrepancy function is directly minimized, starting from random states and tests. By changing an input "seed" integer for the pseudo-random number generator and re-executing, an independent random start is obtained, if an exploration for possible alternative local minima is desired.

N X N matrices, with N = 2,3 or 4 in MATRIXFORMAT, 2 <= N <= 99 in CLSSCLFORMAT. N is user-selected. Large values for the number of states ISTATE, of tests JTEST, or of outcomes of tests will need more memory, run longer, and output more profusely. The 36-bit word structure was not used in the logic; hence the program will probably run on installations with other word lengths.

Running time:
~~ 5 - ~~ 15 min. The longer time includes time for optimized compilation.