Search Talks

Tensor products of normed spaces. From matrix to tensor norms.

After introducing the basic notions about tensors, I will discuss different aspects of quantum entanglement in the framework of tensor norms. I will show how this point of view can bring new insights to this fundamental notion of quantum theory and how new entanglement criteria can be naturally obtained in this way.

The amount of work that can be extracted from a quantum system can be increased by exploiting the information obtained from a measurement performed on a correlated ancillary system. The concept of daemonic ergotropy has been introduced to properly describe and quantify this work extraction enhancement in the quantum regime. We explore the application of this idea in the context of continuously monitored open quantum systems, where information is gained by measuring the environment interacting with the energy-storing quantum device. We show that the corresponding daemonic ergotropy takes values between the ergotropy and the energy of the corresponding unconditional state. The upper bound is achieved by assuming an initial pure state and a perfectly efficient projective measurement on the environment, independently of the kind of measurement performed. On the other hand, if the measurement is inefficient or the initial state is mixed, the daemonic ergotropy is generally dependent on the measurement strategy. We will first theoretically investigate this scenario via a paradigmatic example of an open quantum battery: a two-level atom driven by a classical field and whose spontaneously emitted photons are continuously monitored via either homodyne, heterodyne, or photodetection. We will then present a work-of-principle experimental demonstration of daemonic work extraction by simulating a continuously monitored collision model on an IBM quantum computer.

In this lecture, we provide an introduction to quantum trajectory theory. We present various mathematical problems that arise within this context. In particular, we introduce approaches for analyzing the asymptotic behavior, convergence speed, and stabilization of quantum trajectories toward different states or subspaces through feedback control strategies. Our study includes both quantum non-demolition (QND) measurements and generic (non-QND) measurements in discrete-time and continuous-time settings.

One-dimensional atoms (1D atoms) refer to quantum emitters interacting with light fields confined in a single dimension of space. Owing to the huge number of degrees of freedom of the field, the dynamics of such devices is usually solved in the quantum open system paradigm where the atom (the field) is the system under study (the bath). Recently, so-called Autonomous Collisional Models (ACM) have provided Hamiltonian solutions to the dynamics of 1D atoms, where the atom and the field are two parts of a closed and isolated system. In addition to the interest of providing exact light-atom states, such models are autonomous: the global energy of the system is conserved, allowing for accurate energy balances.

In this talk, I will present a new framework dubbed Bipartite Quantum Energetics (BQE), which allows us to analyse energy exchanges within closed, isolated bipartite systems, and apply it to 1D atoms. In BQE, b-work (b-heat) refer to energy flows induced by effective unitaries (correlations) between systems. I will show that b-work and b-heat are experimentally accessible through -dyne or photon-counting experiments. Focusing on Optical Bloch Equations, I will compare the usual thermodynamic analyses conducted in the open system paradigm to the BQE framework. The two analyses differ by a self-work which yields a tighter expression of the second law, a tightening which I will quantitatively relate to the increased knowledge of the field state. I will finally present experimental results, where energy exchanges between semiconducting quantum dots and light fields have been fully characterized and the self-work was measured. ”

We propose and analyze a universal method to obtain fast charging of a quantum battery by a driven charger system using controlled, pure dephasing of the charger. While the battery displays coherent underdamped oscillations of energy for weak charger dephasing, the quantum Zeno freezing of the charger energy at high dephasing suppresses the rate of transfer of energy to the battery. Choosing an optimum dephasing rate between the regimes leads to a fast charging of the battery. We illustrate our results with the charger and battery modeled by either two-level systems or harmonic oscillators. Apart from the fast charging, the dephasing also renders the charging performance more robust to detuning between the charger, drive, and battery frequencies for the two-level systems case.

1) Introduction to quantum superconducting circuits: resonators, qubits, readout methods
2) Measurement apparatus and their modeling: amplifiers, homodyne and heterodyne measurements, photon detectors, photon counters, quantum efficiency
3) Quantum trajectories of superconducting qubits and cavities: quantum jumps, diffusive trajectories using dispersive measurement and/or fluorescence, past quantum states approach
4) Measurement-based feedback:  stabilization of qubit states and trajectories, stabilization of cavity states, use of neural networks, pros and cons of feedback control compared to reservoir engineering techniques, applications

In order to enable the sequential implementation of quantum information theoretic protocols in the continuous variable framework, we propose two schemes for resource reusability,  resource-splitting protocol and unsharp homodyne measurements. We demonstrate the advantage offered by the first scheme in implementing sequential attempts at continuous variable teleportation when the protocol fails in the previous round. On the other hand, unsharp quadrature measurements are employed to implement the detection of entanglement between several pairs of parties. We exhibit that, under specific conditions, it is possible to witness the entanglement of a state an arbitrary number of times via a scheme that differs significantly from any protocol proposed for finite dimensional systems. 

The investigation of ergodicity or lack thereof in isolated quantum many-body systems has conventionally focused on the description of the reduced density matrices of local subsystems in the contexts of thermalization, integrability, and localization. Recent experimental capabilities to measure the full distribution of quantum states in Hilbert space and the emergence of specific state ensembles have extended this to questions of deep thermalization, by introducing the notion of the projected ensemble – ensembles of pure states of a subsystem obtained by projective measurements on its complement. While previous work examined chaotic unitary circuits, Hamiltonian evolution, and systems with global conserved charges, we study the projected ensemble in systems where there are an extensive number of conserved charges all of which have (quasi)local support. We employ a strongly disordered quantum spin chain which shows many-body localized dynamics over long timescales as well as the ℓ-bit model, a phenomenological archetype of a many-body localized system, with the charges being 1-local in the latter. In particular, we discuss the dependence of the projected ensemble on the measurement basis. Starting with random direct product states, we find that the projected ensemble constructed from time-evolved states converges to a Scrooge ensemble at late times and in the large system limit except when the measurement operator is close to the conserved charges. This is in contrast to systems with global conserved charges where the ensemble varies continuously with the measurement basis. We relate these observations to the emergence of Porter-Thomas distribution in the probability distribution of bitstring measurement probabilities.

We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to quantum jumps between the pointer states associated with the non-demolition measurement. A surprising discovery in earlier work (Tilloy et al., Phys. Rev. A 92, 052111 (2015)) on quantum trajectories with Brownian noise was the phenomena of spikes observed in between the quantum jumps. Here, we show that spikes are observed also for Poisson noise. We consider three cases where the non-demolition is broken by adding, to the basic strong measurement dynamics, either unitary evolution or thermal noise or additional measurements. We present a complete analysis of the spike and jump statistics for all three cases using the fact that the dynamics effectively corresponds to that of stochastic resetting. We provide numerical results to support our analytic results. In addition, we propose protocols for the experimental detection of spikes.

In the presence of environmental decoherence, achieving unit fidelity in quantum state preparation is often unattainable. Monitoring the environment and performing feedback based on the results can enhance the maximum achievable fidelity, yet unit fidelity remains elusive in many scenarios. We derive a theoretical bound on the average fidelity in the ideal case of perfect environmental monitoring. The work focuses on the challenge of preparing Dicke states under collective noise, employing machine learning techniques to identify optimal control protocols. These protocols are then compared against the derived theoretical bound, offering insights into the limits of fidelity in continuously monitored quantum systems.

In continuous measurement, we never have empirical access to the true continuous signal, but rather, to a digitized (discretized) average of the true signal over a finite number time bins. If these time bins are really much smaller than all other time scales, one can reconstruct the quantum trajectory naively with an Euler scheme. Even then, it is just a (good) approximation that cannot be refined. Can one do better? I'll show that one can define a quantum state conditioned on the binned signal (i.e. on a finite list of signal averages), and that, quite surprisingly, this binned conditional state can be efficiently reconstructed. This allows more accurate (in the Bayesian sense) reconstruction of quantum trajectories from data, and can also be used for sampling of trajectories.

Measurements are able to fundamentally affect quantum dynamics. We show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable synchronization at the level of single trajectories. We formulate general criteria for this quantum phenomenon to occur and demonstrate that the number of synchronized realizations can be controlled from none to all. We additionally find that ergodicity is typically broken, since time and ensemble averages may exhibit radically different synchronization behavior. We further introduce a quantum type of multiplexing that involves individual trajectories with distinct synchronization frequencies. Measurement-induced synchronization appears as a genuine nonclassical form of synchrony that exploits quantum superpositions.