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Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a significant challenge, since a state can be entangled with respect to many different of its partitions. We develop a certification pipeline that feeds the statistics of random local measurements into a non-linear dimensionality reduction algorithm, to determine with respect to which partitions a given quantum state is entangled. After training a model on randomly generated quantum states, entangled in different partitions and of varying purity, we verify the accuracy of its predictions on simulated test data, and finally apply it to states prepared on IBM quantum computing hardware., Comment: 15 pages, 5 figures

A recent study [Phys. Rev. B 17 174111 (2022)] has hypothesized the assembly, along a specific type of one-dimensional defects of diamond, of chains of nitrogen-vacancy (NV) centers, potentially enabling the creation of qubit registers via their dipole-coupled electron spins. Here we investigate the connectivity of chains of up to ten coupled spins, mediated by the bi- and multipartite entanglement of their eigenstates. Rather conveniently, for regularly spaced spins the vast majority of the eigenstates displays strong connectivity, especially towards the center of the spectrum and for longer chains. Furthermore, positional disorder can change, and possibly reduce, the connectivity of the register, but seldom suppresses it., Comment: 10 pages, 6 figures

We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show that the statistics of the measured correlators contains sufficient information to characterise the entanglement, and to quantify the mixedness of the state of the computer's register. The transition to the maximally mixed regime, in the embedding space, displays a sharp boundary between entangled and separable states. Away from this boundary, the multipartite entanglement structure is robust to finite noise.

Wave propagation through random continuous media remains an important fundamental problem with applications ranging from remote sensing to quantum communication. Typically, such media are characterized by smooth refractive index fluctuations whose impact on the wave can be captured by the stochastic parabolic equation. The latter can be solved numerically by means of a split-step method, which replaces the continuous medium with a number of discrete phase screens derived from the medium's power spectrum. We introduce and benchmark highly accurate and efficient hybrid phase screens for arbitrary power spectra which are based on the combination of Zernike and Fourier phase screens., Comment: 14 pages, 17 figures

Entanglement and interference are both hallmark effects of quantum physics. Particularly rich dynamics arise when multiple (at least partially) indistinguishable particles are subjected to either of these phenomena. By combining both entanglement and many-particle interference, we propose an interferometric setting through which N-particle interference can be observed, while any interference of lower orders is strictly suppressed. We experimentally demonstrate this effect in a four-photon interferometer, where the interference is nonlocal, in principle, as only pairs of photons interfere at two separate and independent beam splitters. A joint detection of all four photons identifies a high-visibility interference pattern varying as a function of their collective four-particle phase, a genuine four-body property.

A photoelectron, emitted due to the absorption of light quanta as described by the photoelectric effect, is often characterized experimentally by a classical quantity, its momentum. However, since the photoelectron is a quantum object, its rigorous characterization requires the reconstruction of the complete quantum state, the photoelectron's density matrix. Here, we use quantum state tomography to fully characterize photoelectrons emitted from helium and argon atoms upon absorption of ultrashort, extreme ultraviolet light pulses. While in helium we measure a pure photoelectronic state, in argon, spin-orbit interaction induces entanglement between the ion and the photoelectron, leading to a reduced purity of the photoelectron state. Our work shows how state tomography gives new insights into the fundamental quantum aspects of light-induced electronic processes in matter, bridging the fields of photoelectron spectroscopy and quantum information, and offering new spectroscopic possibilities for quantum technology.

We study the Hong-Ou-Mandel interference of two identical, composite particles, each formed of two bosonic or fermionic constituents, as they scatter against a potential barrier in a one-dimensional lattice. For tightly bound composites, we show that the combination of their constituents' mutual interactions and exchange symmetry gives rise to an effective nearest-neighbour interaction between composites, which induces a reduction of the interference contrast.

We describe the Hong-Ou-Mandel interference of two identical particles evolving on a one-dimensional tight-binding lattice where a potential barrier plays the role of a beam splitter. Careful consideration of the symmetries underlying the two-particle interference effect allows us to reformulate the problem in terms of ordinary wave interference in a Michelson interferometer. This approach is easily generalized to the case where the particles interact, and we compare the resulting analytical predictions for the bunching probability to numerical simulations of the two-particle dynamics.

Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on additional assumptions on the input state of the interferometer, such as, for instance, a fixed mode occupation, nor on any assumption on the degrees of freedom that potentially make the particles distinguishable. We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability, and derive tight lower bounds on it that can be efficiently measured in experiments. Moreover, we present a consistent definition of perfect distinguishability and characterize the corresponding set of states. In particular, we show that these states are diagonal in the computational basis up to a permutationally invariant unitary. Moreover, we find that convex combinations of states that describe partially distinguishable and perfectly indistinguishable particles can lead to perfect distinguishability, which itself is not preserved under convex combinations.

Certifying the performance of quantum computers requires standardized tests. We propose a simple energy estimation benchmark that is motivated from quantum chemistry. With this benchmark we statistically characterize the noisy outcome of the IBM Quantum System One in Ehningen, Germany. We find that the benchmark results hardly correlate with the gate errors and readout errors reported for the device. In a time-resolved analysis, we monitor the device over several hours and find two-hour oscillations of the benchmark results, as well as outliers, which we cannot explain from the reported device status. We then show that the implemented measurement error mitigation techniques cannot resolve these oscillations, which suggests that deviations from the theoretical benchmark outcome statistics do not stem solely from the measurement noise of the device.

We study the transport of many partially distinguishable and possibly interacting particles under the action of repeated projective measurements on a target space and investigate how the particles' interference affects the mean first detection time. We contrast the detection of exactly $n$ versus at least $n$ particles, explain divergences in the mean first detection time through spectral properties of the generating evolution operator, and illustrate our findings by an example., Comment: Comments are welcome

We unveil the signature of many-body interference across dynamical regimes of the Bose-Hubbard model. Increasing the particles' indistinguishability enhances the temporal fluctuations of few-body observables, with a dramatic amplification at the onset of quantum chaos. By resolving the exchange symmetries of partially distinguishable particles, we explain this amplification as the fingerprint of the initial state's coherences in the eigenbasis., Comment: 5 pages, 2 figures + supplemental material

We tailor the quantum statistics of a bosonic field to deterministically drive a quantum system into a target state. Experimentally accessible states of the field achieve good control of multi-level or -qubit systems, notably also at coupling strengths beyond the rotating-wave approximation. This extends optimal control theory to the realm of fully quantized, strongly coupled control and target degrees of freedom.

We port the concept of non-Markovian quantum dynamics to the many-particle realm, by a suitable decomposition of the many-particle Hilbert space. We show how the specific structure of many-particle states determines the observability of non-Markovianity by single- or many-particle observables, and discuss a realization in a readily implementable few-particle set-up.

Structured light offers wider bandwidths and higher security for communication. However, propagation through complex random media, such as the Earth's atmosphere, typically induces intermodal crosstalk. We show numerically and experimentally that coupling of photonic orbital angular momentum (OAM) modes is governed by a universal function of a single parameter -- the ratio between the random medium's and the beam's transverse correlation lengths, even in the regime of pronounced intensity fluctuations., Comment: 5 pages, 4 figures (without Supplemental Material) or 12 pages, 14 figures (with Supplemental Material)

The dependence of the chaotic phase of the Bose-Hubbard Hamiltonian on particle number $N$, system size $L$ and particle density is investigated in terms of spectral and eigenstate features. We analyze the development of the chaotic phase as the limit of infinite Hilbert space dimension is approached along different directions, and show that the fastest route to chaos is the path at fixed density $n \lesssim 1$. The limit $N \to \infty$ at constant $L$ leads to a slower convergence of the chaotic phase towards the random matrix theory benchmarks. In this case, from the distribution of the eigenstate generalized fractal dimensions, the ergodic phase becomes more distinguishable from random matrix theory for larger $N$, in a similar way as along trajectories at fixed density., Comment: 9 pages, 8 figures

We show that instantaneous spatial singular modes of light in a dynamically evolving, turbulent atmosphere offer significantly improved high-fidelity signal transmission as compared to standard encoding bases corrected by adaptive optics. Their enhanced stability in stronger turbulence is associated with a subdiffusive algebraic decay of the transmitted power with evolution time., Comment: 6 pages, 4 figures (article) and 7 pages, 6 figures (supplemental material)

We propose a continuous variable quantum state tomography protocol of electrons which result from the ionization of atoms or molecules by the absorption of extreme ultraviolet light pulses. Our protocol is benchmarked against a direct calculation of the quantum state of photoelectrons ejected from helium and argon in the vicinity of a Fano resonance. In the latter case, we furthermore distill ion-photoelectron entanglement due to spin-orbit splitting. This opens new routes towards the investigation of quantum coherence and entanglement properties on the ultrafast timescale.

We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime., Comment: 13 pages, 9 figures

We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions, and identify sufficient conditions under which low-order correlators fully characterize many-body coherences, as controlled by the constituents' mutual distinguishability. Comparison of correlators of different order detects many-body entanglement., Comment: 5 pages, 2 figures + supplemental material (1 page)

We investigate optimal states of photon pairs to excite a target transition in a multilevel quantum system. With the help of coherent control theory for two-photon absorption with quantum light, we infer the maximal population achievable by optimal entangled vs. separable states of light. Interference between excitation pathways, as well as the presence of nearby states, may hamper the selective excitation of a particular target state, but we show that quantum correlations can help to overcome this problem, and enhance the achievable "selectivity" between two energy levels, i.e. the relative difference in population transferred into each of them. We find that the added value of optimal entangled states of light increases with broadening linewidths of the target states., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in E. G. Carnio et al., J. Chem. Phys. 154, 214114 (2021) and may be found at https://doi.org/10.1063/5.0049863

We investigate how entanglement can enhance two-photon absorption in a three-level system. First, we employ the Schmidt decomposition to determine the entanglement properties of the optimal two-photon state to drive such a transition, and the maximum enhancement which can be achieved in comparison to the optimal classical pulse. We then adapt the optimization problem to realistic experimental constraints, where photon pairs from a down-conversion source are manipulated by local operations such as spatial light modulators. We derive optimal pulse shaping functions to enhance the absorption efficiency, and compare the maximal enhancement achievable by entanglement to the yield of optimally shaped, separable pulses., Comment: 25 pages, 8 figures

In the general framework of open quantum systems, we assess the impact of the pulse area on single and double quantum coherence (1QC and 2QC) signals extracted from fluorescence emitted by dilute thermal gases. We show that 1QC and 2QC signals are periodic functions of the pulse area, with distinctive features which reflect the particles' interactions via photon exchange, the polarizations of the laser pulses, and the observation direction., Comment: 11 pages, 4 figures

Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by Boson Sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal towards the practical implementation of quantum technologies. Here we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the - a priori unknown - optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations., Comment: 15 pages, 12 figures

We show how to characterize the indistinguishability of up to four identical, bosonic or fermionic particles, which are rendered partially distinguishable through their internal degrees of freedom prepared in mixed states. This is accomplished via their counting statistics when subjected to a highly symmetric unitary acting upon their external (i.e., dynamical) degrees of freedom. For pure internal states, we further extract information on the particles' collective phases, which ultimately allows for an experimental reconstruction of the full many-particle density operator up to complex conjugation.

We investigate, in a four photon interference experiment in a laser-written waveguide structure, how symmetries control the suppression of many-body output events of a $J_x$ unitary. We show that totally destructive interference does not require mutual indistinguishability between all, but only between symmetrically paired particles, in agreement with recent theoretical predictions. The outcome of the experiment is well described by a quantitative simulation which accounts for higher order emission of the photon source, imbalances in the scattering network, partial distinguishability, and photon loss., Comment: 14 pages, 7 figures

We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The eigenvectors are shown to become ergodic in the thermodynamic limit, in the configuration space Fock basis, in which random matrix theory offers a remarkable description of their typical structure. The distributions of the generalized fractal dimensions, however, are ever more distinguishable from random matrix theory as the Hilbert space dimension grows., Comment: 4 pages, 4 figures + supplemental material

We develop a framework to systematically investigate the influence of many-particle interference on the dynamics of generic $-$ possibly interacting $-$ bosonic systems. We consider mixtures of bosons which belong to several distinguishable species, allowing us to tune the level of many-particle interference, and identify the corresponding signatures in the time-dependent expectation values of observables. Interference contributions to these expectation values can be classified based on the number of interfering particles. Interactions are shown to generate a series of additional, higher-order interference contributions. Finally, based on a decomposition of the Hilbert space of partially distinguishable bosons into irreducible representations of the unitary group, we determine some spectral characteristics of (in)distinguishability.

A comprehensive description of molecular electron transfer reactions is essential for our understanding of fundamental phenomena in bio-energetics and molecular electronics. Experimental studies of molecular systems in condensed-phase environments, however, face difficulties to independently control the parameters that govern the transfer mechanism with high precision. We show that trapped-ion experiments instead allow to reproduce and continuously connect vastly different regimes of molecular charge transfer through precise tuning of, e.g., phonon temperature, electron-phonon interactions, and electronic couplings. Such a setting allows not only to reproduce widely-used transport models, such as Marcus theory. It also provides access to transfer regimes that are unattainable for molecular experiments, while controlling and measuring the relevant observables on the level of individual quanta. Our numerical simulations predict an unconventional quantum transfer regime, featuring a transition from quantum adiabatic- to resonance-assisted transfer as a function of the donor-acceptor energy gap, that can be reached by increasing the electronic coupling at low temperatures. Trapped ion-based quantum simulations thus promise to enhance our microscopic understanding of molecular electron transfer processes, and may help to reveal efficient design principles for synthetic devices., Comment: 11 pages, 6 figures

We perform a systematic investigation of variational forms (wave function Ans\"atze), to determine the ground state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic boundary conditions), using the Variational Quantum Eigensolver (VQE) algorithm. In particular, we focus on the nature of the entangler blocks which provide the most efficient convergence to the system ground state inasmuch as they use the minimal number of gate operations, which is key for the implementation of this algorithm in NISQ computers. Using the concurrence measure, the amount of entanglement of the register qubits is monitored during the entire optimization process, illuminating its role in determining the efficiency of the convergence. Finally, we investigate the scaling of the VQE circuit depth as a function of the desired energy accuracy. We show that the number of gates required to reach a solution within an error $\varepsilon$ follows the Solovay-Kitaev scaling, $\mathcal{O}(\log^c(1/\varepsilon))$, with an exponent $c = 1.31 {\rm{\pm}}0.13$., Comment: 14 pages, 5 figures

We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled $m\times m$ bipartite quantum state, after propagation under an entanglement-preserving $n \times n$ ($n\geq m$) unitary. Truncation -- physically enforced, e.g., by a detector's finite cross section -- projects the state onto an $s \times s$-dimensional subspace ($3\leq s \leq n$). For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of $n$, $m$ and $s$., Comment: 10 pages, 4 figures, comments are welcome

Manifestations of dipole-dipole interactions in dilute thermal gases are difficult to sense because of strong inhomogeneous broadening. Recent experiments reported signatures of such interactions in fluorescence detection-based measurements of multiple quantum coherence (MQC) signals, with many characteristic features hitherto unexplained. We develop an original open quantum systems theory of MQC in dilute thermal gases, which allows us to resolve this conundrum. Our theory accounts for the vector character of the atomic dipoles as well as for driving laser pulses of arbitrary strength, includes the far-field coupling between the dipoles, which prevails in dilute ensembles, and effectively incorporates atomic motion via a disorder average. We show that collective decay processes -- which were ignored in previous treatments employing the electrostatic form of dipolar interactions -- play a key role in the emergence of MQC signals., Comment: 33 pages, 6 figures

When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance., Comment: 6 pages, 4 figures

We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time, and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the time scale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process., Comment: 15 pages, 12 figures

We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behaviour of the particles launched either at the single particle ground state or saddle point energy, in a time-independent potential. We complement these results by a characterisation of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time-evolution of a single particle's von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (\textsc{Mctdh-x}) -- which also allows us to extrapolate our results for increasing particle numbers., Comment: 20 pages, 14 figures

We study the diffraction of two maximally entangled qubits encoded into spatial modes of light with orbital angular momenta $\pm \hbar l_0$, on angular apertures. Exploiting the uncertainty relation between angular position and momentum, we quantify the diffraction-induced entanglement loss, for different $l_0$, as a function of the angular uncertainty $\Delta \phi$ induced by the apertures. We demonstrate that the degradation of entanglement follows a universal law parametrised by the product $l_0\Delta \phi$ alone.} {We study the diffraction of two photonic qubits, which are initially maximally entangled in their orbital angular momenta, on angular apertures. Using the uncertainty relation between angular position and momentum, we show that the diffraction-induced entanglement losses exhibit universal behaviour., Comment: 10 pages, 4 figures, updated version as accepted for publication in journal of optics, comments are welcome

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous, and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states---a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement., Comment: 9 pages, 6 figures + 3 pages supplemental material, 2 figures

Multi-particle interference is a key resource for quantum information processing, as exemplified by Boson Sampling. Hence, given its fragile nature, an essential desideratum is a solid and reliable framework for its validation. However, while several protocols have been introduced to this end, the approach is still fragmented and fails to build a big picture for future developments. In this work, we propose an operational approach to validation that encompasses and strengthens the state of the art for these protocols. To this end, we consider the Bayesian hypothesis testing and the statistical benchmark as most favorable protocols for small- and large-scale applications, respectively. We numerically investigate their operation with finite sample size, extending previous tests to larger dimensions, and against two adversarial algorithms for classical simulation: the Mean-Field sampler and the Metropolized Independent Sampler. To evidence the actual need for refined validation techniques, we show how the assessment of numerically simulated data depends on the available sample size, as well as on the internal hyper-parameters and other practically relevant constraints. Our analyses provide general insights into the challenge of validation, and can inspire the design of algorithms with a measurable quantum advantage., Comment: 10 pages, 7 figures

Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and biology, whether that fundamental quantum nature may condition the dynamical and functional system properties on mesoscopic if not macroscopic scales. But which are the distinctive signatures of quantum properties in complex systems, notably when modulated by environmental stochasticity and dynamical instabilities? It appears that, to settle this question across the above communities, a shared understanding is needed of the central feature of quantum mechanics: wave-particle duality. In this Perspective, we elaborate how randomness induced by this very quantum property can be discerned from the stochasticity ubiquitous in complex systems already on the classical level. We argue that in the study of increasingly complex systems such distinction requires the analysis of single incidents of quantum dynamical processes., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in the Journal of Physical Chemistry Letters, copyright (c) American Chemical Society after peer review. To access the final edited and published work see https://pubs.acs.org/articlesonrequest/AOR-kG4qqCAtGSTG86tqZwdw

We study the entanglement evolution of photonic orbital angular momentum qubit states with opposite azimuthal indices $l_0$, in a weakly turbulent atmosphere. Using asymptotic methods, we deduce analytical expressions for the amplitude of turbulence-induced crosstalk between the modes $l_0$ and $-l_0$. Furthermore, we analytically establish distinct, universal entanglement decay laws for Kolmogorov's turbulence model and for two approximations thereof., Comment: 11 pages, 3 figures

We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wave- and particle-like properties balance each other. Much as in the well-understood single-particle case, which-way information -- here on the level of many-particle paths -- lends particle-character, while interference -- here due to coherent superpositions of many-particle amplitudes -- indicates wave-like properties. We analyze how many-particle which-way information, continuously tunable by the level of distinguishability of fermionic or bosonic, identical and possibly interacting particles, constrains interference contributions to many-particle observables and thus controls the quantum-to-classical transition in many-particle quantum systems. The versatility of our theoretical framework is illustrated for Hong-Ou-Mandel- and Bose-Hubbard-like exemplary settings.

We outline the non-perturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows, for the first time, a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light and the coherent backscattering peak's height with increasing pump intensity. Our theory establishes a general, microscopic, scalable approach to nonlinear transport phenomena in complex quantum materials., Comment: 33 pages, 21 figures

We demonstrate many-body multifractality of the Bose-Hubbard Hamiltonian's ground state in Fock space, for arbitrary values of the interparticle interaction. Generalized fractal dimensions unambiguously signal, even for small system sizes, the emergence of a Mott insulator, that cannot, however, be naively identified with a localized phase in Fock space. We show that the scaling of the derivative of any generalized fractal dimension with respect to the interaction strength encodes the critical point of the superfluid to Mott insulator transition, and provides an efficient way to accurately estimate its position. We further establish that the transition can be quantitatively characterized by one single wavefunction amplitude from the exponentially large Fock space., Comment: Main text (5 pages, 6 figures) + Supplemental material (2 pages, 2 figures)

We study the potential of adaptive optics (AO) to protect entanglement of high-dimensional photonic orbital-angular-momentum (OAM) states against turbulence-induced phase distortions. We demonstrate that AO is able to reduce crosstalk among the OAM modes and, consequently, the entanglement decay as well as photon losses. A test of the AO-stabilized output state against high-dimensional Bell inequalities shows that the transmitted entanglement allows for secure communication, even in the strong scintillation regime., Comment: 20 pages, 6 figures

We demonstrate that the output statistics of a quantum annealing protocol run on D-Wave 2000Q can be explained by static disorder garnishing an otherwise ideal device hardware. A Boltzmann-like distribution over distinct output states emerges with increasing problem size, and significantly reduces the chances for a correct identification of the sought-after optimal solutions.

Several distinct classes of unitary mode transformations have been known to exhibit the strict suppression of a large set of transmission events, as a consequence of totally destructive many-particle interference. In another work [Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by identifying a general class of unitary matrices which exhibit such interferences. Here, we provide a detailed theoretical analysis that substantially expands on all aspects of this generalisation: We prove the suppression laws put forward in our other paper, establish how they interrelate with forbidden single-particle transitions, show how all suppression laws hitherto known can be retrieved from our general formalism, and discuss striking differences between bosons and fermions. Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable., Comment: 16 pages, 4 figures

In a general, multi-mode scattering setup, we show how the permutation symmetry of a many-particle input state determines those scattering unitaries which exhibit strictly suppressed many-particle transition events. We formulate purely algebraic suppression laws that identify these events and show that the many-particle interference at their origin is robust under weak disorder and imperfect indistinguishability of the interfering particles. Finally, we demonstrate that all suppression laws so far described in the literature are embedded in the general framework that we here introduce., Comment: 6 pages, 2 figures

We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases: commuting system and interaction Hamiltonians, the short-time limit, and the Markov approximation., Comment: 5 pages, 1 figure

We provide an analytical expression for the entanglement decay of initially maximally entangled orbital angular momentum bi-photon states, when scattered off an obstruction. We show that the decay is controlled by the diffraction-induced mutual overlap between the diffracted field modes, and quantify its dependence on the size and position of the obstruction., Comment: 8 pages, 5 figures