Abstract
| Language | English |
|---|---|
| Article number | 043016 |
| Number of pages | 85 |
| Journal | New Journal of Physics |
| Volume | 13 |
| Issue number | April |
| DOIs | |
| Publication status | Published - Apr 2011 |
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Keywords
- computational physics
- quantum observables
- categorical algebra
- diagrammatics
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Interacting quantum observables : categorical algebra and diagrammatics. / Coecke, Bob; Duncan, Ross.
In: New Journal of Physics, Vol. 13, No. April, 043016 , 04.2011.Research output: Contribution to journal › Article
TY - JOUR
T1 - Interacting quantum observables
T2 - New Journal of Physics
AU - Coecke, Bob
AU - Duncan, Ross
PY - 2011/4
Y1 - 2011/4
N2 - This paper has two tightly intertwined aims: (i) to introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatize complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an Abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z- and X-spin observables, which yields a scaled variant of a bialgebra.
AB - This paper has two tightly intertwined aims: (i) to introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatize complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an Abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z- and X-spin observables, which yields a scaled variant of a bialgebra.
KW - computational physics
KW - quantum observables
KW - categorical algebra
KW - diagrammatics
U2 - 10.1088/1367-2630/13/4/043016
DO - 10.1088/1367-2630/13/4/043016
M3 - Article
VL - 13
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
IS - April
M1 - 043016
ER -