of common eigenstates. Note that there can be some simultaneous eigenstates of and , but not enough in number to constitute a complete basis. The canonical commutation relation implies that this applies to position and momentum. Likewise, an analogous relationship holds for any two of the spin observables defined by the Pauli matrices; measurements of spin along perpendicular axes are complementary. This has been generalized to discrete observables with more than two possible outcomes using mutually unbiased bases, which provide complementary observables defined on finite-dimensional Hilbert spaces. See also Copenhagen interpretation Canonical coordinates Conjugate variables Interpretations of quantum mechanics Measurement in quantum mechanics Wave–particle duality References Further reading Berthold-Georg Englert, Marlan O. Scully & Herbert Walther, Quantum Optical Tests of Complementarity, Nature, Vol 351, pp 111–116 (9 May 1991) and (same authors) The Duality in Matter and Light Scientific American, pg 56–61, (December 1994). Niels Bohr, Causality and Complementarity: supplementary papers edited by Jan Faye and Henry J. Folse. The Philosophical Writings of Niels Bohr, Volume IV. Ox Bow Press. 1998. External links Discussions with Einstein on Epistemological Problems in Atomic Physics Einstein's Reply to Criticisms Quantum mechanics Niels Bohr Dichotomies Scientific laws