TY - JOUR AB - Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “sufficiently free” rational points of bounded height on arbitrary smooth projective hypersurfaces of low degree that are defined over the rationals. AU - Browning, Timothy D AU - Sawin, Will ID - 9007 IS - 4 JF - Commentarii Mathematici Helvetici SN - 00102571 TI - Free rational points on smooth hypersurfaces VL - 95 ER - TY - JOUR AB - Microwave photonics lends the advantages of fiber optics to electronic sensing and communication systems. In contrast to nonlinear optics, electro-optic devices so far require classical modulation fields whose variance is dominated by electronic or thermal noise rather than quantum fluctuations. Here we demonstrate bidirectional single-sideband conversion of X band microwave to C band telecom light with a microwave mode occupancy as low as 0.025 ± 0.005 and an added output noise of less than or equal to 0.074 photons. This is facilitated by radiative cooling and a triply resonant ultra-low-loss transducer operating at millikelvin temperatures. The high bandwidth of 10.7 MHz and total (internal) photon conversion efficiency of 0.03% (0.67%) combined with the extremely slow heating rate of 1.1 added output noise photons per second for the highest available pump power of 1.48 mW puts near-unity efficiency pulsed quantum transduction within reach. Together with the non-Gaussian resources of superconducting qubits this might provide the practical foundation to extend the range and scope of current quantum networks in analogy to electrical repeaters in classical fiber optic communication. AU - Hease, William J AU - Rueda Sanchez, Alfredo R AU - Sahu, Rishabh AU - Wulf, Matthias AU - Arnold, Georg M AU - Schwefel, Harald G.L. AU - Fink, Johannes M ID - 9114 IS - 2 JF - PRX Quantum SN - 2691-3399 TI - Bidirectional electro-optic wavelength conversion in the quantum ground state VL - 1 ER - TY - JOUR AB - Quantum transduction, the process of converting quantum signals from one form of energy to another, is an important area of quantum science and technology. The present perspective article reviews quantum transduction between microwave and optical photons, an area that has recently seen a lot of activity and progress because of its relevance for connecting superconducting quantum processors over long distances, among other applications. Our review covers the leading approaches to achieving such transduction, with an emphasis on those based on atomic ensembles, opto-electro-mechanics, and electro-optics. We briefly discuss relevant metrics from the point of view of different applications, as well as challenges for the future. AU - Lauk, Nikolai AU - Sinclair, Neil AU - Barzanjeh, Shabir AU - Covey, Jacob P AU - Saffman, Mark AU - Spiropulu, Maria AU - Simon, Christoph ID - 9194 IS - 2 JF - Quantum Science and Technology SN - 2058-9565 TI - Perspectives on quantum transduction VL - 5 ER - TY - JOUR AB - We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen--Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems. AU - Fischer, Julian L AU - Laux, Tim AU - Simon, Theresa M. ID - 9039 IS - 6 JF - SIAM Journal on Mathematical Analysis SN - 00361410 TI - Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies VL - 52 ER - TY - JOUR AB - We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5]. AU - Bao, Zhigang AU - Erdös, László AU - Schnelli, Kevin ID - 9104 JF - Journal d'Analyse Mathematique SN - 00217670 TI - On the support of the free additive convolution VL - 142 ER - TY - GEN AB - This dataset comprises all data shown in the plots of the main part of the submitted article "Bidirectional Electro-Optic Wavelength Conversion in the Quantum Ground State". Additional raw data are available from the corresponding author on reasonable request. AU - Hease, William J AU - Rueda Sanchez, Alfredo R AU - Sahu, Rishabh AU - Wulf, Matthias AU - Arnold, Georg M AU - Schwefel, Harald AU - Fink, Johannes M ID - 13071 TI - Bidirectional electro-optic wavelength conversion in the quantum ground state ER - TY - JOUR AB - Quantum information technology based on solid state qubits has created much interest in converting quantum states from the microwave to the optical domain. Optical photons, unlike microwave photons, can be transmitted by fiber, making them suitable for long distance quantum communication. Moreover, the optical domain offers access to a large set of very well‐developed quantum optical tools, such as highly efficient single‐photon detectors and long‐lived quantum memories. For a high fidelity microwave to optical transducer, efficient conversion at single photon level and low added noise is needed. Currently, the most promising approaches to build such systems are based on second‐order nonlinear phenomena such as optomechanical and electro‐optic interactions. Alternative approaches, although not yet as efficient, include magneto‐optical coupling and schemes based on isolated quantum systems like atoms, ions, or quantum dots. Herein, the necessary theoretical foundations for the most important microwave‐to‐optical conversion experiments are provided, their implementations are described, and the current limitations and future prospects are discussed. AU - Lambert, Nicholas J. AU - Rueda Sanchez, Alfredo R AU - Sedlmeir, Florian AU - Schwefel, Harald G. L. ID - 9195 IS - 1 JF - Advanced Quantum Technologies SN - 2511-9044 TI - Coherent conversion between microwave and optical photons - An overview of physical implementations VL - 3 ER - TY - JOUR AB - Distributed ledgers provide high availability and integrity, making them a key enabler for practical and secure computation of distributed workloads among mutually distrustful parties. Many practical applications also require strong confidentiality, however. This work enhances permissioned and permissionless blockchains with the ability to manage confidential data without forfeiting availability or decentralization. The proposed Calypso architecture addresses two orthogonal challenges confronting modern distributed ledgers: (a) enabling the auditable management of secrets and (b) protecting distributed computations against arbitrage attacks when their results depend on the ordering and secrecy of inputs. Calypso introduces on-chain secrets, a novel abstraction that enforces atomic deposition of an auditable trace whenever users access confidential data. Calypso provides user-controlled consent management that ensures revocation atomicity and accountable anonymity. To enable permissionless deployment, we introduce an incentive scheme and provide users with the option to select their preferred trustees. We evaluated our Calypso prototype with a confidential document-sharing application and a decentralized lottery. Our benchmarks show that transaction-processing latency increases linearly in terms of security (number of trustees) and is in the range of 0.2 to 8 seconds for 16 to 128 trustees. AU - Kokoris Kogias, Eleftherios AU - Alp, Enis Ceyhun AU - Gasser, Linus AU - Jovanovic, Philipp AU - Syta, Ewa AU - Ford, Bryan ID - 9011 IS - 4 JF - Proceedings of the VLDB Endowment TI - CALYPSO: Private data management for decentralized ledgers VL - 14 ER - TY - JOUR AB - Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [Phys. Rev. B 93, 014203 (2016)] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions—so-called “bubbles”—resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states, we demonstrate the stability of many-body localization with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in the Bose-Hubbard model. AU - Brighi, Pietro AU - Abanin, Dmitry A. AU - Serbyn, Maksym ID - 8308 IS - 6 JF - Physical Review B SN - 2469-9950 TI - Stability of mobility edges in disordered interacting systems VL - 102 ER - TY - JOUR AB - We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix. AU - Bao, Zhigang AU - Erdös, László AU - Schnelli, Kevin ID - 10862 IS - 7 JF - Journal of Functional Analysis KW - Analysis SN - 0022-1236 TI - Spectral rigidity for addition of random matrices at the regular edge VL - 279 ER -