Abstract
Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.
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Notes
Use the fact that:
$$e^{-2iS_z P_d/nh^2} \frac{1}{\sqrt{2}} (| 0 \rangle _i+ | 1 \rangle _i) = \frac{1}{\sqrt{2}} (e^{-i P_d/nh}| 0 \rangle _i +e^{i P_d/nh}| 1 \rangle _i).$$Use the fact that e ix≈1+ix for x small enough, and this is guaranteed by n big enough.
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Acknowledgements
We wish to thank the Interdisciplinary Center (IDC) in Herzliya for their hospitality at the academic year 2009–2010. We also wish to thank Daniel Rohlich for his explanations.
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Tamir, B., Masis, S. Weak Measurement and Weak Information. Found Phys 42, 531–543 (2012). https://doi.org/10.1007/s10701-012-9624-1
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DOI: https://doi.org/10.1007/s10701-012-9624-1