| 1. |
- Appleby, D.M., et al.
(författare)
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Systems of Imprimitivity for the Clifford Group
- 2014
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Ingår i: Quantum information & computation. - : Rinton Press. - 1533-7146. ; 14:3-4, s. 339-360
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Tidskriftsartikel (refereegranskat)abstract
- It is known that if the dimension is a perfect square the Clifford group can be represented by monomial matrices. Another way of expressing this result is to say that when the dimension is a perfect square the standard representation of the Clifford group has a system of imprimitivity consisting of one dimensional subspaces. We generalize this result to the case of an arbitrary dimension. Let k be the square-free part of the dimension. Then we show that the standard representation of the Clifford group has a system of imprimitivity consisting of k-dimensional subspaces. To illustrate the use of this result we apply it to the calculation of SIC-POVMs (symmetric informationally complete positive operator valued measures), constructing exact solutions in dimensions 8 (hand-calculation) as well as 12 and 28 (machine-calculation).
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| 2. |
- Appleby, D. M., et al.
(författare)
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The monomial representations of the Clifford group
- 2012
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Ingår i: Quantum information & computation. - : Rinton Press, Inc.. - 1533-7146. ; 12:5-6, s. 404-431
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Tidskriftsartikel (refereegranskat)abstract
- We show that the Clifford group-the normaliser of the Weyl-Heisenberg group-can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.
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| 3. |
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| 4. |
- de Nooijer, Wesley, et al.
(författare)
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Evaluation of Arctic warming in mid-Pliocene climate simulations
- 2020
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Ingår i: Climate of the Past. - : Copernicus GmbH. - 1814-9324 .- 1814-9332. ; 16:6, s. 2325-2341
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Tidskriftsartikel (refereegranskat)abstract
- Palaeoclimate simulations improve our understanding of the climate, inform us about the performance of climate models in a different climate scenario, and help to identify robust features of the climate system. Here, we analyse Arctic warming in an ensemble of 16 simulations of the mid-Pliocene Warm Period (mPWP), derived from the Pliocene Model Intercomparison Project Phase 2 (PlioMIP2). The PlioMIP2 ensemble simulates Arctic (60-90 degrees N) annual mean surface air temperature (SAT) increases of 3.7 to 11.6 degrees C compared to the pre-industrial period, with a multimodel mean (MMM) increase of 7.2 degrees C. The Arctic warming amplification ratio relative to global SAT anomalies in the ensemble ranges from 1.8 to 3.1 (MMM is 2.3). Sea ice extent anomalies range from -3.0 to -10.4 x 10(6) km(2), with a MMM anomaly of -5.6 x 10 6 km(2), which constitutes a decrease of 53 % compared to the pre-industrial period. The majority (11 out of 16) of models simulate summer seaice-free conditions (<= 1 x 10(6) km(2)) in their mPWP simulation. The ensemble tends to underestimate SAT in the Arctic when compared to available reconstructions, although the degree of underestimation varies strongly between the simulations. The simulations with the highest Arctic SAT anomalies tend to match the proxy dataset in its current form better. The ensemble shows some agreement with reconstructions of sea ice, particularly with regard to seasonal sea ice. Large uncertainties limit the confidence that can be placed in the findings and the compatibility of the different proxy datasets. We show that while reducing uncertainties in the reconstructions could decrease the SAT data-model discord substantially, further improvements are likely to be found in enhanced boundary conditions or model physics. Lastly, we compare the Arctic warming in the mPWP to projections of future Arctic warming and find that the PlioMIP2 ensemble simulates greater Arctic amplification than CMIP5 future climate simulations and an increase instead of a decrease in Atlantic Meridional Overturning Circulation (AMOC) strength compared to pre-industrial period. The results highlight the importance of slow feedbacks in equilibrium climate simulations, and that caution must be taken when using simulations of the mPWP as an analogue for future climate change.
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