The joint measurement problem

According to orthodox quantum theory, the joint measurement of noncommuting observables is impossible. It has been claimed recently that such joint measurements are admitted in a generalized formalism for quantum theory developed by Ludwig and Davies, by means of so-called ‘unsharp observables.’ It is argued in this paper that this claim has not been substantiated.

[1]  Peter Mittelstaedt,et al.  Unsharp particle-wave duality in a photon split-beam experiment , 1987 .

[2]  L. Lugiato.  Theory of open systems I , 1975 .

[3]  H. Doebner,et al.  On the equivalence of nonrelativistic quantum mechanics based upon sharp and fuzzy measurements , 1976 .

[4]  Jean-Marc Lévy-Leblond,et al.  Who is afraid of nonhermitian operators? A quantum description of angle and phase , 1976 .

[5]  P. Busch,et al.  On the reality of spin and helicity , 1989 .

[6]  Gérard G. Emch,et al.  Fuzzy observables in quantum mechanics , 1974 .

[7]  Paul Busch,et al.  Indeterminacy relations and simultaneous measurements in quantum theory , 1985 .

[8]  Paul Busch,et al.  On various joint measurements of position and momentum observables in quantum theory , 1984 .

[9]  W. D. Muynck,et al.  The inaccuracy principle , 1990 .

[10]  Compatible stochastic observables that do not commute , 1985 .

[11]  S. T. Ali.  Stochastic localization, quantum mechanics on phase space and quantum space-time , 1985 .

[12]  P. Dirac,et al.  THE MATHEMATICAL FOUNDATIONS OF QUANTUM THEORY , 1978 .

[13]  Paul Busch.  Some realizable joint measurements of complementary observables , 1987 .

[14]  C. Y. She,et al.  Simultaneous Measurement of Noncommuting Observables , 1966 .

[15]  Lawrence M. Seiford,et al.  Recent developments in dea : the mathematical programming approach to frontier analysis , 1990 .

[16]  V. S. Varadarajan,et al.  Probability in Physics and a Theorem on Simultaneous Observability , 1962 .

[17]  C. Ross.  Found , 1869, The Dental register.

[18]  P. Busch,et al.  Some remarks on effects, operations, and unsharp measurements , 1989 .

[19]  A. R. Marlow,et al.  Mathematical foundations of quantum theory , 1978 .

[20]  F. Schroeck.  On the stochastic measurement of incompatible spin components , 1982 .

[21]  E. Prugovec̆ki.  Stochastic Quantum Mechanics And Quantum Spacetime , 1984 .

[22]  Paul Busch,et al.  A Note on Quantum Theory, Complementarity, and Uncertainty , 1985, Philosophy of Science.

[23]  Milburn,et al.  Interpretation for a positive P representation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[24]  Jouni Viiri.  Symposium on the foundations of modern physics 1990 , 1989 .

[25]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[26]  F. Schroeck.  Coexistence of observables , 1989 .

[27]  J. Neumann.  Mathematische grundlagen der Quantenmechanik , 1935 .

[28]  Eduard Prugove ki,et al.  Probability measures on fuzzy events in phase space , 1976 .

[29]  R. Persaud.  Philosophy of science , 1992, The Lancet.

[30]  W. D. Muynck,et al.  Nonideal quantum measurements , 1990 .