arXiv subjects

Mattia Walschaers

Publications and source records attributed to Mattia Walschaers.

At least 37 records · Page 2Linked to original sources

arXiv2023

Resources for bosonic quantum computational advantage

Quantum computers promise to dramatically outperform their classical counterparts. However, the non-classical resources enabling such computational advantages are challenging to pinpoint, as it is not a single resource but the subtle interplay of many that can be held responsible for these potential advantages. In this work, we show that every bosonic quantum computation can be recast into a continuous-variable sampling computation where all computational resources are contained in the input state. Using this reduction, we derive a general classical algorithm for the strong simulation of bosonic computations, whose complexity scales with the non-Gaussian stellar rank of both the input state and the measurement setup. We further study the conditions for an efficient classical simulation of the associated continuous-variable sampling computations and identify an operational notion of non-Gaussian entanglement based on the lack of passive separability, thus clarifying the interplay of bosonic quantum computational resources such as squeezing, non-Gaussianity and entanglement.

quant-ph↗

arXiv2023

Practical tests for sub-Rayleigh source discriminations with imperfect demultiplexers

Quantum-optimal discrimination between one and two closely separated light sources can be achieved by ideal spatial-mode demultiplexing, simply monitoring whether a photon is detected in a single antisymmetric mode. However, we show that for any, no matter how small, imperfections of the demultiplexer, this simple statistical test becomes practically useless, i.e. as good as flipping a coin. While we identify a class of separation-independent tests with vanishing error probabilities in the limit of large numbers of detected photons, they are generally unreliable beyond that very limit. As a practical alternative, we propose a simple semi-separation-independent test, which provides a method for designing reliable experiments, through arbitrary control over the maximal probability of error.

quant-ph↗

arXiv2023

Gaussian quantum metrology for mode-encoded parameters

Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.

quant-ph↗

arXiv2022

Homodyne detection of non-Gaussian quantum steering

Quantum correlations are at the core of current developments in quantum technologies. Certification protocols of entanglement and steering, suitable for continuous-variable non-Gaussian states are scarce and generally highly demanding from an experimental point of view. We propose a protocol based on Fisher information for witnessing steering in general continuous-variable bipartite states, through homodyne detection. It proves to be relevant for the detection of non-Gaussian steering in scenarios where witnesses based on Gaussian features like the covariance matrix are shown to fail.

quant-ph↗

arXiv2022

Emergent complex quantum networks in continuous-variables non-Gaussian states

We use complex network theory to study a class of continuous-variable quantum states that present both multipartite entanglement and non-Gaussian statistics. We consider the intermediate scale of several dozens of components at which such systems are already hard to characterize. In particular, the states are built from an initial imprinted cluster state created via Gaussian entangling operations according to a complex network structure. We then engender non-Gaussian statistics via multiple photon subtraction operations acting on a single node. We replicate in the quantum regime some of the models that mimic real-world complex networks in order to test their structural properties under local operations. We then go beyond the already known single-mode effects, by studying the emergent network of photon-number correlations via complex networks measures. We analytically prove that the imprinted network structure defines a vicinity of nodes, at a distance of four steps from the photon-subtracted node, in which the emergent network changes due to photon subtraction. Moreover, our numerical analysis shows that the emergent structure is greatly influenced by the structure of the imprinted network. Indeed, while the mean and the variance of the degree and clustering distribution of the emergent network always increase, the higher moments of the distributions are governed by the specific structure of the imprinted network. Finally, we show that the behaviour of nearest neighbours of the subtraction node depends on how they are connected to each other in the imprinted structure.

quant-ph↗

arXiv2022

Quantum limits for resolving Gaussian sources

We determine analytically the quantum Cramér-Rao bound for the estimation of the separation between two point sources in arbitrary Gaussian states. Our analytical expression is valid for arbitrary sources brightness, and it allows to determine how different resources, such as mutual coherence (induced by thermal correlations or displacement) or squeezing affect the scaling of the ultimate resolution limit with the mean number of emitted photons. In practical scenarios, we find coherent states of the sources to achieve quantum optimal resolution.

quant-ph↗

arXiv2022

Maximal entanglement increase with single-photon subtraction

Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the Rényi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.

quant-ph↗

arXiv2021

Resolving Mutually Coherent Bright Point-Sources

We analyze the problem of resolving two point-sources in the case of mutually coherent sources with arbitrary quantum statistics, mutual phase, relative and absolute intensity. We use a sensitivity measure based on the method of moments and compare direct imaging with spatial mode demultiplexing, analytically proving the advantage of the latter. We show that the sensitivity of spatial mode demultiplexing saturates the quantum Fisher information, for all known cases, even for non-Gaussian states of the sources.

quant-ph↗

arXiv2021

Non-Gaussian Quantum States and Where to Find Them

Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states. We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems. We then use this framework in various ways to explore the structure of the state space. We explain how non-Gaussian states can be characterised not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank. For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations. To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state. Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states. On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations. Finally, we will demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage. At the end of the Tutorial, we also provide an overview of several experimental realisations of non-Gaussian quantum states in quantum optics and beyond.

quant-ph↗

arXiv2021

Moment-based superresolution: Formalism and applications

Sensitivity limits are usually determined using the Cramér-Rao bound. Recently this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits, usually require the full measurement statistics, which can be challenging to access. In this work, we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources, and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial mode demultiplexing. For demultiplexing, our method is optimal, i.e. it saturates the quantum Cramér-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity and on the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cramér-Rao bound even in the presence of noise.

quant-ph↗

arXiv2021

Optimal observables and estimators for practical superresolution imaging

Recent works identified resolution limits for the distance between incoherent point sources. However, it remains unclear how to choose suitable observables and estimators to reach these limits in practical situations. Here, we show how estimators saturating the Cramér-Rao bound for the distance between two thermal point sources can be constructed using an optimally designed observable in the presence of practical imperfections, such as misalignment, crosstalk and detector noise.

quant-ph↗

arXiv2021

Response of quantum spin networks to attacks

We investigate the ground states of spin models defined on networks that we imprint (e.g. non-complex random networks like Erdos-Renyi or complex networks like Watts-Strogatz, and Barabasi-Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counterintuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems, possibly even a robust quantum Internet in the long run, that is maximally resistant to decoherence.

quant-ph↗

arXiv2021

Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering

Wigner negativity, as a well-known indicator of nonclassicality, plays an essential role in quantum computing and simulation using continuous-variable systems. Recently, it has been proven that Einstein-Podolsky-Rosen steering is a prerequisite to generate Wigner negativity between two remote modes. Motivated by the demand of real-world quantum network, here we investigate the shareability of generated Wigner negativity in the multipartite scenario from a quantitative perspective. By establishing a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality, we show that the amount of Wigner negativity cannot be freely distributed among different modes. Moreover, for photon subtraction -- one of the main experimentally realized non-Gaussian operations -- we provide a general method to quantify the remotely generated Wigner negativity. With this method, we find that there is no direct quantitative relation between the Gaussian steerability and the amount of generated Wigner negativity. Our results pave the way for exploiting Wigner negativity as a valuable resource for numerous quantum information protocols based on non-Gaussian scenario.

quant-ph↗

arXiv2021

Experimental statistical signature of many-body quantum interference

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.

quant-ph↗

arXiv2021

Conditional preparation of non-Gaussian quantum optical states by mesoscopic measurement

Non-Gaussian states of an optical field are important as a proposed resource in quantum information applications. While conditional preparation is a highly successful approach to preparing such states, their quality is limited by detector non-idealities such as dead time, narrow dynamic range, limited quantum efficiency and dark noise. Mesoscopic photon counters, with peak performance at higher photon number, offer many practical advantages over single-photon level conditioning detectors. Here we propose a novel approach involving displacement of the ancilla field into the regime where mesoscopic detectors can be used. We explore this strategy theoretically and present simulations accounting for experimental non-idealities such as loss and amplification noise, showing that precise photon-number resolution is not necessary to herald highly nonclassical states. We conclude that states with strong Wigner negativity can be prepared at high rates by this technique under experimentally attainable conditions.

quant-ph↗

arXiv2021

Full characterization of the transmission properties of a multi-plane light converter

Multi-plane light conversion allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the number of modes transmitted by a multi-plane light converter (MPLC) is extremely large. In this work, we aim to characterize the transmission properties of a multi-plane light converter inside and, for the first time, outside the design-modes subspace. By numerically reconstructing the transmission matrix of such systems, we individuate new ways to evaluate their efficiency in performing the design transformation. Moreover, we develop an analytical random matrix model that suggests that in the regime of a large number of shaped modes an MPLC behaves like a random scattering medium with limited number of controlled channels.

physics.optics↗

arXiv2020

Certification of non-Gaussian states with operational measurements

We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous variable quantum states.

quant-ph↗

arXiv2020

Quantum state engineering in arrays of nonlinear waveguides

In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., Phys. Rev. Appl. $\bf{14}$, 044025 (2020). We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization and scalability of spatial linear cluster states.

quant-ph↗