



01776nas a2200181   4500008004100000245004200041210004100083260001400124520125200138653002701390653003101417100002301448700002301471700002001494700002201514700002101536856003701557       2022                        eng d00aContinuous-Variable Shadow Tomography0 aContinuousVariable Shadow Tomography  c11/9/20223 a<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>10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGandhari, Srilekha1 aAlbert, Victor, V.1 aGerrits, Thomas1 aTaylor, Jacob, M.1 aGullans, Michael  uhttps://arxiv.org/abs/2211.0514901811nas a2200205   4500008004100000245005900041210005900100260001300159490000600172520120100178653002701379653003501406653003101441100001601472700002101488700001501509700001901524700002501543856003701568       2022                        eng d00aUniversal scattering with general dispersion relations0 aUniversal scattering with general dispersion relations  c4/6/20220 v43 a<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>10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)1 aWang, Yidan1 aGullans, Michael1 aNa, Xuesen1 aWhitsitt, Seth1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2103.09830