Sequentially independent effects
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- by Stan Gudder and Gabriel Nagy
- Proc. Amer. Math. Soc. 130 (2002), 1125-1130
- DOI: https://doi.org/10.1090/S0002-9939-01-06194-9
- Published electronically: October 1, 2001
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Abstract:
A quantum effect is a yes-no measurement that may be unsharp. An effect is represented by an operator $E$ on a Hilbert space that satisfies $0\le E\le I$. We define effects $E_1,E_2,\ldots ,E_n$ to be sequentially independent if the result of any sequential measurement of $E_1,E_2,\ldots ,E_n$ does not depend on the order in which they are measured. We show that two effects are sequentially independent if and only if they are compatible. That is, their corresponding operators commute. We also show that three effects are sequentially independent if and only if all permutations of the product of their corresponding operators coincide. It is noted that this last condition does not imply that the three effects are mutually compatible.References
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Bibliographic Information
- Stan Gudder
- Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
- Email: sgudder@cs.du.edu
- Gabriel Nagy
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- Email: nagy@math.ksu.edu
- Received by editor(s): September 19, 2000
- Received by editor(s) in revised form: October 27, 2000
- Published electronically: October 1, 2001
- Additional Notes: The second author was partially supported by NSF grant DMS 9706858
- Communicated by: Joseph A. Ball
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1125-1130
- MSC (2000): Primary 47B15, 47B65; Secondary 81P10, 81P15
- DOI: https://doi.org/10.1090/S0002-9939-01-06194-9
- MathSciNet review: 1873787