Mattia Walschaers

Optimally Designed Quantum Transport across Disordered Networks

We establish a general mechanism for highly efficient quantum transport through finite, disordered 3D networks. It relies on the interplay of disorder with centrosymmetry and a dominant doublet spectral structure and can be controlled by the proper tuning of only coarse-grained quantities. Photosynthetic light harvesting complexes are discussed as potential biological incarnations of this design principle.

Statistical benchmark for BosonSampling

Boson samplers-set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modes-promise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.

Entanglement and Wigner function negativity of multimode non-Gaussian states

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

From Many-Particle Interference to Correlation Spectroscopy

Identical particles are of profound importance in nature: Pauli’s exclusion principle for fermions forms the cornerstone of chemistry, whereas bosonic quantum statistics allows us to prepare Bose-Einstein condensates and induces Planck’s law of black body radiation. As such, quantum statistics describes fundamental symmetry properties of quantum states of identical particles, in equilibrium. Yet, it turns out that the quantum dynamics of identical particles holds additional and non-trivial surprises, due to intricate interference phenomena on the level of many-particle transition amplitudes. The simplest manifestation thereof is the by now well-established Hong-Ou-Mandel (HOM) interference dip [1, 2] which is observed when two photons are transmitted through a balanced beam splitter. However, it recently has been realised that HOM is only the tip of the iceberg of a whole zoo of many-particle interference phenomena [3{18], with many particles transmitted through many, randomly coupled modes as the other (truly complex) extreme, of potential relevance for photonic quantum simulation and/or computation [19{23]. Hence, many-particle interference denes a new, wide, and rather unexplored area of quantum eects

Statistical theory of designed quantum transport across disordered networks.

We explain how centrosymmetry, together with a dominant doublet of energy eigenstates in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalization of the chaos-assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behavior of characteristic statistical properties with the size of the network. We show that these analytical predictions compare well to numerical simulations, using Hamiltonians sampled from the Gaussian orthogonal ensemble.

On optimal currents of indistinguishable particles

We establish a mathematically rigorous, general and quantitative framework to describe currents of non- (or weakly) interacting, indistinguishable particles driven far from equilibrium. We derive tight upper and lower bounds for the achievable fermionic and bosonic steady state current, respectively, which can serve as benchmarks for special cases of interacting many-particle dynamics. For fermionic currents, we identify a symmetry-induced enhancement mechanism in parameter regimes where the coupling between system and reservoirs is weak. This mechanism is broadly applicable provided the inter-particle interaction strength is small as compared to typical exchange interactions.

Statistical signatures of multimode single-photon-added and -subtracted states of light

The addition or subtraction of a photon from a Gaussian state of light is a versatile and experimentally feasible procedure to create non-Gaussian states. In multimode setups, these states manifest a wide range of phenomena when the photon is added or subtracted in a mode-tunable way. In this contribution, we derive the truncated correlations, which are multimode generalisations of cumulants, between quadratures in different modes as statistical signatures of these states. These correlations are then used to obtain the full multimode Wigner function, the properties of which are subsequently studied. In particular we investigate the effect of impurity in the subtraction or addition process, and evaluate its impact on the negativity of the Wigner function. Finally, we elaborate on the generation of inherent entanglement through subtraction or addition of a photon from a pure squeezed vacuum.

QUANTUM TRANSPORT IN BIOLOGICAL FUNCTIONAL UNITS: NOISE, DISORDER, STRUCTURE

Through simulations of quantum coherent transport on disordered molecular networks, we show that three dimensional structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations. Furthermore, configurations that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

Scattering theory of efficient quantum transport across finite networks

We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned networks sites allows to significantly accelerate the excitation transfer processes as compared to a dimer structure, if only the disordered Hamiltonians are constrained to be centrosymmetric, and to exhibit a dominant doublet in their spectrum. We identify the cause of this efficiency enhancement in the constructive interplay between disorder-induced fluctuations of the dominant doublets splitting and the coupling strength between the input and output sites to the scattering channels. We find that the characteristic strength of these fluctuations together with the channel coupling fully control the transfer efficiency.

Signature of multi-photon interference in boson sampling experiments

The progressive development of quantum technologies in many areas, ranging from investigation on foundamentals of quantum of mechanics to quantum information and computation, has increased the interest on those problems that can exhibit a quantum advantage. The Boson Sampling problem is a clear example where traditional computers fail in the task of sampling from the distribution of n indistinguishable photons after a propagation in a m-mode optical interferometer. In this context, in the absence of classical algorithms able to simulate efficiently multi-photon interference, the validation of Boson Sampling is still an open problem. Here we investigate a novel approach to Boson Sampling validation based on statistical properties of correlation functions. In particular we discuss its feasibility in actual proof-of-principle experiments. Furthermore we provide an extensive study of the physical resources required to validate experiments, investigating also the role of bosonic bunching in high-dimensional applications. Our investigation confirms the goodness of the validation protocol, paving the way to use this toolbox for the validation of Boson Sampling devices.