arXiv subjects

Valentin Gebhart

Publications and source records attributed to Valentin Gebhart.

13 recordsLinked to original sources

arXiv2024

Fundamental bounds for parameter estimation with few measurements

Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist bounds such as the Cram\'er-Rao bound (CRB) become questionable. Here, we discuss different linear (Barankin-like) conditions that can be imposed on estimators and analyze when these conditions admit an optimal estimator with finite variance, for any number of measurement repetitions. We show that, if the number of imposed conditions is larger than the number of measurement outcomes, there generally does not exist a corresponding estimator with finite variance. We analyze this result from different viewpoints and examples and elaborate on connections to the shot-noise limit and the Kitaev phase estimation algorithm. We then derive an extended Cram\'er-Rao bound that is compatible with a finite variance in situations where the Barankin bound is undefined. Finally, we show an exemplary numerical confrontation between frequentist and Bayesian approaches to parameter estimation.

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arXiv2023

Entanglement Harvesting from Electromagnetic Quantum Fields

In many states of the quantum electromagnetic field, including the vacuum state, entanglement exists between different space-time regions -- even space-like separated ones. These correlations can be harvested and, thereby, detected by quantum systems which locally interact with the field. Here, we propose an experimental implementation of such an entanglement-harvesting scheme which is based on electro-optic sampling (EOS). We demonstrate that state-of-the-art EOS experiments enable one to harvest entanglement from the vacuum field and to study quantum correlations within general THz fields. We further show how Bell nonlocality present in the vacuum field can be probed. Finally, we introduce a novel approach to mitigate shot noise in single-beam EOS configurations. These findings pave the way for experimental inquiries into foundational properties of relativistic quantum field theory, and empower EOS as a diagnostic tool in THz quantum optics.

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arXiv2023

Creating nonlocality using geometric phases between partially distinguishable photons

The geometric (Berry-Pancharatnam) phase originates from the intrinsic geometry of the space of quantum states and can be observed in different situations, such as a cyclic evolution of a quantum system. Here, we utilize the geometric phase to obtain a surprising insight: It is possible to create nonlocal correlations in a fixed interferometer with independent photon inputs by varying the photons' internal states.In particular, we consider a cyclic interferometer that is fixed, i.e., that has no variable internal phase shifts or subsequent measurement settings. Instead, the measurement choices of the different parties correspond to the internal states of the input photons which influence the observed correlations via a collective $N$-photon geometric phase, constituting a different approach for the generation of nonlocality with respect to the usual paradigm. We observe a trade-off between the geometric phases and the visibility of the many-photon interference, impeding the generation of nonlocality. However, by making use of the dynamical quantum Zeno effect, we show that nonlocality can be created in the fixed cyclic interferometer using 12 (or more) independent photons.

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arXiv2023

Learning Quantum Systems

The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks.

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arXiv2023

Extending the fair sampling assumption using causal diagrams

Discarding undesirable measurement results in Bell experiments opens the detection loophole that prevents a conclusive demonstration of nonlocality. As closing the detection loophole represents a major technical challenge for many practical Bell experiments, it is customary to assume the so-called fair sampling assumption (FSA) that, in its original form, states that the collectively postselected statistics are a fair sample of the ideal statistics. Here, we analyze the FSA from the viewpoint of causal inference: We derive a causal structure that must be present in any causal model that faithfully encapsulates the FSA. This provides an easy, intuitive, and unifying approach that includes different accepted forms of the FSA and underlines what is really assumed when using the FSA. We then show that the FSA can not only be applied in scenarios with non-ideal detectors or transmission losses, but also in ideal experiments where only parts of the correlations are postselected, e.g., when the particles' destinations are in a superposition state. Finally, we demonstrate that the FSA is also applicable in multipartite scenarios that test for (genuine) multipartite nonlocality.

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arXiv2022

Coincidence postselection for genuine multipartite nonlocality: Causal diagrams and threshold efficiencies

Genuine multipartite nonlocality (GMN), the strongest form of multipartite nonlocality that describes fully collective nonlocal correlations among all experimental parties, can be observed when different distant parties each locally measure a particle from a shared entangled many-particle state. For the demonstration of GMN, the experimentally observed statistics are typically postselected: Events for which some parties do not detect a particle must be discarded. This coincidence postselection generally leads to the detection loophole that invalidates a proper nonlocality demonstration. In this work, we address how to close the detection loophole for a coincidence detection in demonstrations of nonlocality and GMN. We first show that if the number of detected particles is conserved, i.e., using ideal and noiseless experimental devices, one can employ causal diagrams and the no-signalling principle to prove that a coincidence postselection cannot create any detection loophole. Furthermore, for realistic experimental devices with finite detection efficiencies, we show how a general Bell inequality can be sharpened such that its new version is still valid after a postselection of the measurement data. In this case, there are threshold detection efficiencies that, if surpassed in the experiment, lead to the possibility to demonstrate nonlocality and GMN without opening the detection loophole. Our results imply that genuine $N$-partite nonlocality can be generated from $N$ independent particle sources even when allowing for non-ideal detectors.

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arXiv2022

Genuine multipartite nonlocality with causal-diagram postselection

The generation and verification of genuine multipartite nonlocality (GMN) is of central interest for both fundamental research and quantum technological applications, such as quantum privacy. To demonstrate GMN in measurement data, the statistics are commonly postselected by neglecting undesired data. Until now, valid postselection strategies have been restricted to local postselection. A general postselection that is decided after communication between parties can mimic nonlocality, even though the complete data are local. Here, we establish conditions under which GMN is demonstrable even if observations are postselected collectively. Intriguingly, certain postselection strategies that require communication among several parties still offer a demonstration of GMN shared between all parties. The results are derived using the causal structure of the experiment and the no-signalling condition imposed by relativity. Finally, we apply our results to show that genuine three-partite nonlocality can be created with independent particle sources.

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arXiv2021

Casimir-Polder interaction of neutrons with metal or dielectric surfaces

We predict a repulsive Casimir-Polder-type dispersion interaction between a single neutron and a metal or dielectric surface. We consider a scenario where a single neutron is subject to an external magnetic field. Due to its intrinsic magnetic moment, the neutron then forms a magnetisable two-level system which can exchange virtual photons with a nearby surface. The resulting dispersion interaction between a purely magnetic object (neutron) and a purely electric one (surface) is found to be repulsive, in contrast to the typical attractive interaction between electric objects. Its magnitude is considerably smaller than the standard atom--surface Casimir-Polder force due to the magnetic nature of the interaction and the smallness of the electron-to-neutron mass ratio. Nevertheless, we show that it can be comparable to the gravitational potential of the same surface and should be taken into consideration in future neutron interference experiments.

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arXiv2021

Bayesian Quantum Multiphase Estimation Algorithm

Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a single phase, applications to the simultaneous estimation of several phases may bring substantial advantages; for instance, in the presence of spatial or temporal constraints. In this work, we study a Bayesian algorithm for the parallel (simultaneous) estimation of multiple arbitrary phases. The protocol gives access to correlations in the Bayesian multi-phase distribution resulting in covariance matrix elements scaling inversely proportional to the square of the total number of quantum resources. The parallel estimation allows to surpass the sensitivity of sequential single-phase estimation strategies for optimal linear combinations of phases. Furthermore, the algorithm proves a certain noise resilience and can be implemented using single photons and standard optical elements in currently accessible experiments.

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arXiv2021

Identifying nonclassicality from experimental data using artificial neural networks

The fast and accessible verification of nonclassical resources is an indispensable step towards a broad utilization of continuous-variable quantum technologies. Here, we use machine learning methods for the identification of nonclassicality of quantum states of light by processing experimental data obtained via homodyne detection. For this purpose, we train an artificial neural network to classify classical and nonclassical states from their quadrature-measurement distributions. We demonstrate that the network is able to correctly identify classical and nonclassical features from real experimental quadrature data for different states of light. Furthermore, we show that nonclassicality of some states that were not used in the training phase is also recognized. Circumventing the requirement of the large sample sizes needed to perform homodyne tomography, our approach presents a promising alternative for the identification of nonclassicality for small sample sizes, indicating applicability for fast sorting or direct monitoring of experimental data.

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arXiv2021

Quantifying Computational Advantage of Grover's Algorithm with the Trace Speed

Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover's search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.

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arXiv2020

Neural-network approach for identifying nonclassicality from click-counting data

Machine-learning and neural-network approaches have gained huge attention in the context of quantum science and technology in recent years. One of the most essential tasks for the future development of quantum technologies is the verification of nonclassical resources. Here, we present an artificial neural network approach for the identification of nonclassical states of light based on recorded measurement statistics. In particular, we implement and train a network which is capable of recognizing nonclassical states based on the click statistics recorded with multiplexed detectors. We use simulated data for training and testing the network, and we show that it is capable of identifying some nonclassical states even if they were not used in the training phase. Especially, in the case of small sample sizes, our approach can be more sensitive in identifying nonclassicality than established criteria which suggests possible applications in presorting of experimental data and online applications.

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arXiv2020

Topological transition in measurement-induced geometric phases

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.

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