



@article {3182,
	title = {Continuous-Variable Shadow Tomography},
	year = {2022},
	month = {11/9/2022},
	abstract = {<p>Shadow tomography is a framework for constructing succinct descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable tomography in the classical-shadow framework, obtaining rigorous bounds on the sample complexity for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N5) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.</p>},
	keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)},
	doi = {10.48550/ARXIV.2211.05149},
	url = {https://arxiv.org/abs/2211.05149},
	author = {Gandhari, Srilekha and Victor V. Albert and Gerrits, Thomas and Taylor, Jacob M. and Michael Gullans}
}
@article {3030,
	title = {Universal scattering with general dispersion relations},
	journal = {Phys. Rev. Research},
	volume = {4},
	year = {2022},
	month = {4/6/2022},
	chapter = {023014},
	abstract = {<p>Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension D\&ge;1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=\&plusmn;|d|km, where m\&ge;2 is an integer. For a large class of these problems for any positive integer m, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\&rarr;0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D\&ge;1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.</p>},
	keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)},
	doi = {https://doi.org/10.1103/PhysRevResearch.4.023014},
	url = {https://arxiv.org/abs/2103.09830},
	author = {Wang, Yidan and Michael Gullans and Na, Xuesen and Whitsitt, Seth and Alexey V. Gorshkov}
}
