Quantum Reality and Measurement: A Quantum Logical Approach

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context.

[1]  M. Ozawa.  Quantum measuring processes of continuous observables , 1984 .

[2]  N. Bohr.  II - Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , 1935 .

[3]  Masanao Ozawa.  Perfect correlations between noncommuting observables , 2005 .

[4]  Bas C. van Fraassen,et al.  Current Issues in Quantum Logic , 1981 .

[5]  Masanao Ozawa.  Transfer principle in quantum set theory , 2007, J. Symb. Log..

[6]  Masanao Ozawa,et al.  Physical content of Heisenberg's uncertainty relation: limitation and reformulation , 2003 .

[7]  E. B. Davies.  Quantum theory of open systems , 1976 .

[8]  Leslie E Ballentine,et al.  The statistical interpretation of quantum mechanics , 1970 .

[9]  M. Ozawa.  Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement , 2002, quant-ph/0207121.

[10]  N. Bohr.  The Quantum Postulate and the Recent Development of Atomic Theory , 1928, Nature.

[11]  S. Gudder,et al.  Joint Distributions of Observables , 1968 .

[12]  Gaisi Takeuti,et al.  Quantum Set Theory , 1981 .

[13]  G. Temple.  The physical principles of the quantum theory , 1932 .

[14]  Masanao Ozawa.  UNCERTAINTY PRINCIPLE FOR QUANTUM INSTRUMENTS AND COMPUTING , 2003 .

[15]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[16]  Masanao Ozawa.  Uncertainty relations for noise and disturbance in generalized quantum measurements , 2003 .

[17]  E. Stachow.  An Operational Approach to Quantum Probability , 1978 .

[18]  Masanao Ozawa.  Quantum perfect correlations , 2006 .

[19]  J. Neumann,et al.  The Logic of Quantum Mechanics , 1936 .

[20]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.