Journal of Physics A: Mathematical and Theoretical
We give a necessary and sufficient condition for the incompatibility of a pair of effects in a ge... more We give a necessary and sufficient condition for the incompatibility of a pair of effects in a general probabilistic model in which the state space is a total convex space, which can be obtained by minimising a real parameter. This has an interpretation in terms of the least noise that must be included to make the given pair compatible.
Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from va... more Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from various perspectives. We emphasise the many mathematical structures intimately related to Kochen-Specker proofs, ranging through functional analysis, sheaf theory and topos theory, Coxeter groups and algebraic geometry. Some novel results are presented along the way.
In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the ... more In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspective-neutral approach to QRF covariance to general unimodular Lie groups. This is a framework that links internal QRF perspectives via a manifestly gauge-invariant Hilbert space in the form of"quantum coordinate transformations", and we clarify how it is a quantum extension of special covariance. We model the QRF orientations as coherent states which give rise to a covariant POVM, furnishing a consistent probability interpretation and encompassing non-ideal QRFs whose orientations are not perfectly distinguishable. We generalize the construction of relational observables, establish a variety of their algebraic properties and equip them with a transparent conditional probability interpretation. We import the distinction between gauge transformations and physical symmetries from gaug...
M. Hamed Mohammady,1, 2 Takayuki Miyadera,3 and Leon Loveridge4 1QuIC, École Polytechnique de Bru... more M. Hamed Mohammady,1, 2 Takayuki Miyadera,3 and Leon Loveridge4 1QuIC, École Polytechnique de Bruxelles, CP 165/59, Université Libre de Bruxelles, 1050 Brussels, Belgium 2RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia 3Department of Nuclear Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan 4Quantum Technology Group, Department of Science and Industry Systems, University of South-Eastern Norway, 3616 Kongsberg, Norway
Journal of Physics A: Mathematical and Theoretical
We give a necessary and sufficient condition for the incompatibility of a pair of effects in a ge... more We give a necessary and sufficient condition for the incompatibility of a pair of effects in a general probabilistic model in which the state space is a total convex space, which can be obtained by minimising a real parameter. This has an interpretation in terms of the least noise that must be included to make the given pair compatible.
Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from va... more Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from various perspectives. We emphasise the many mathematical structures intimately related to Kochen-Specker proofs, ranging through functional analysis, sheaf theory and topos theory, Coxeter groups and algebraic geometry. Some novel results are presented along the way.
In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the ... more In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspective-neutral approach to QRF covariance to general unimodular Lie groups. This is a framework that links internal QRF perspectives via a manifestly gauge-invariant Hilbert space in the form of"quantum coordinate transformations", and we clarify how it is a quantum extension of special covariance. We model the QRF orientations as coherent states which give rise to a covariant POVM, furnishing a consistent probability interpretation and encompassing non-ideal QRFs whose orientations are not perfectly distinguishable. We generalize the construction of relational observables, establish a variety of their algebraic properties and equip them with a transparent conditional probability interpretation. We import the distinction between gauge transformations and physical symmetries from gaug...
M. Hamed Mohammady,1, 2 Takayuki Miyadera,3 and Leon Loveridge4 1QuIC, École Polytechnique de Bru... more M. Hamed Mohammady,1, 2 Takayuki Miyadera,3 and Leon Loveridge4 1QuIC, École Polytechnique de Bruxelles, CP 165/59, Université Libre de Bruxelles, 1050 Brussels, Belgium 2RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava 84511, Slovakia 3Department of Nuclear Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan 4Quantum Technology Group, Department of Science and Industry Systems, University of South-Eastern Norway, 3616 Kongsberg, Norway
Symmetries and Groups in Contemporary Physics, Proceedings, The XXIXth International Colloquium on Group-Theoretical Methods in Physics
We revisit the theorem of Wigner, Araki and Yanase (WAY) describing limitations to repeatable qua... more We revisit the theorem of Wigner, Araki and Yanase (WAY) describing limitations to repeatable quantum measurements that arise from the presence of conservation laws. We will review a strengthening of this theorem by exhibiting and discussing a condition that has hitherto not been identified as a relevant factor. We will also show that an extension of the theorem to continuous variables such as position and momentum can be obtained if the degree of repeatability is suitably quantified.
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