Search Talks

In this talk, we study how noise and quantum monitoring shape symmetry breaking and chaos. We discuss the simulation of complex open quantum systems using classical noise and how noise limits adiabatic strategies, giving rise to anti-Kibble-Zurek scaling. We further show how spontaneous symmetry breaking is modified in the presence of an observer whose action is described by continuous quantum measurements. In the second part of the talk, we show how the signatures of Hamiltonian quantum chaos in the spectral form factor are suppressed energy dephasing while they are enhanced when the dynamics is conditioned to the absence of con quantum jumps.

Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the ramifications of cSSR and fusion rules in anyonic quantum information theory remain largely unexplored. In this talk, we unveil that the information-theoretic characteristics of anyons diverge fundamentally from those of non-anyonic systems such as qudits, bosons, and fermions and display intricate structures. In bipartite anyonic systems, pure states may have different marginal spectra, and mixed states may contain pure marginal states. More striking is that in a bipartite pure entangled state, parties may lack equal access to entanglement. This we call entanglement disparity, and it is manifested in asymmetric quantum teleportation employing an entangled anyonic state shared between Alice and Bob, where Alice can perfectly teleport unknown quantum information to Bob, but Bob lacks this capability. These traits challenge conventional understanding, necessitating new approaches to characterize quantum information and correlations in anyons. We expect that these distinctive features will also be present in non-Abelian lattice gauge field theories. Our findings significantly advance the understanding of the information-theoretic aspects of anyons and may lead to realizations of quantum communication and cryptographic protocols where one party holds sway over the other.

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.

Recent developments in the architecture of quantum computers have enabled their use in applications for various information-processing tasks. This information becomes unreliable primarily due to the erroneous implementation of control methods for state preparation and measurements and the qubit’s inability to store information for long periods in the presence of uncontrollable noise sources. Conventional noise spectroscopy protocols can characterize and model environmental noise but are usually resource-intensive and lengthy. Moreover, the underlying noise can vary over time, making noise profile extraction futile as this new information cannot be harnessed to improve quantum error correction or dynamical decoupling protocols. In this work, we address this challenge using a machine learning-based methodology to swiftly extract noise spectra of multiple qubits and demonstrate a possible noise mitigation strategy. The procedure involves implementing undemanding dynamical decoupling sequences to record coherence decays of the investigated qubits and then predict the underlying noise spectra with the help of a convolution neural network pre-trained on a synthetic dataset. The protocol is virtually hardware-agnostic. However, we validated its effectiveness using IBM’s superconducting qubits. We used these rapidly obtained yet accurate noise spectra to design bespoke dynamic decoupling sequences and perform time-dependent noise spectroscopy.

A variable-range interacting Ising model with spin-$s$ particles exhibits distinct behavior depending on the fall-off rates in the range of interactions, notably non-local (NL), quasi-local (QL), and local, which are based on the equilibrium properties.  It is unknown if such a transition is respected in the dynamical framework. We use an analytically solvable model in arbitrary spatial dimension ($D$), to establish a dynamical non-local (dNL) behavior, which does not agree with the known result of equilibrium NL behavior. We analyze the profiles of topological entanglement entropy (TEE), mutual information, Lieb-Robinson bound (LRB) and genuine multipartite entanglement (GME) of the weighted graph state (WGS), prepared when the multi-level maximally coherent state at each site evolves according to the long-range spin-$s$ Ising Hamiltonian. Specifically, we demonstrate that the connection between the LRB profile and the divergence in the first derivative of GME with respect to the fall-off rate in the WGS can indicate the transition point from dNL to a dynamical local/quasi-local (dQL) regimes.

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.

Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a non-infinitesimal time resolution. In this work, we propose a systematic assessment of the accuracy of a map. We perform error analyses for diffusive quantum trajectories, based on single-time-step Kraus operators proposed in the literature, and find the orders in time increment to which such operators satisfy the conditions for valid average quantum evolution (completely positive, convex-linear, and trace-preserving), and the orders to which they match the Lindblad solutions. Given these error analyses, we propose a Kraus operator that satisfies the valid average quantum evolution conditions and agrees with the Lindblad master equation, to second order in the time increment, thus surpassing all other existing approaches. In order to test how well our proposed operator reproduces exact quantum trajectories, we analyze two examples of qubit measurement, where exact maps can be derived: a qubit subjected to a dispersive (z-basis) measurement and a fluorescence (dissipative) measurement. We show analytically that our proposed operator gives the smallest average trace distance to the exact quantum trajectories, compared to existing approaches.

In this talk, I will consider a finite-level quantum system linearly coupled to a bosonic reservoir, that is the prototypical example of an open quantum system. I will present recent results on the reduced dynamics of the finite system when the coupling constant tends to infinity, i.e. in the ultrastrong coupling limit. In particular, I will show that the dynamics corresponds to a nonselective projective measurement followed by a unitary evolution with an effective (Zeno) Hamiltonian. I will also discuss the connection with the usual setting for the quantum Zeno effect, based on repeated measurements.
The rigorous proof of the limit is quite simple and can be generalized to the case of a small system interacting with two reservoirs when one of the couplings is finite and the other one tends to infinity. In this second scenario the reduced dynamics is richer and possibly non-Markovian.
Joint work with Marco Merkli, arXiv:2411.06817.    

Entanglement of pure and mixed quantum states.

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.

We consider weak unitary symmetries of Markovian open quantum systems at the level of the joint dynamics of the system and its environment described by a continuous matrix product state, as well as for stochastic quantum trajectories of the system, obtained by conditioning on counting measurements of the environment. We derive necessary and sufficient conditions under which the dynamics of these different descriptions exhibit a weak symmetry, in turn characterising the resulting symmetries of their generators. In particular, this depends on whether the counting measurement satisfies the conditions we derive. In doing so we also consider the possible gauge transformations for generators of quantum trajectories, i.e. when two representations of the master operator produce equivalent trajectory ensembles.

We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling. This unraveling picture corresponds to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation in the single-shot scenario. Finally, we consider the case where some information is lost in data compression/post-selection, and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.

Quantum experiments are performed in noisy platforms. In NISQ devices, realistic setups can be described by open systems or noisy Hamiltonians. Using this setup, we explore a number of dynamical schemes and control techniques. First, starting from a generic noisy Hamiltonian, I will show how noise can help simulate long-range and many-body interaction in a quantum platform [1]. Second, in the setup of shortcut to adiabaticity extended to open quantum systems, we adapt our noisy Hamiltonian to control the thermalization of a harmonic oscillator [2] and generate a squeezed thermal state [3] in arbitrary time. 

Third, adding non-Hermiticity in the picture [3], I will show how noise allows for a rich control of the dynamics, and induced a new phase in which the lossy state becomes stable. More generally, we characterize the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. 

Finally, I will briefly show results where we do not look at the noise-averaged density matrix but at an observable introduced as the stochastic operator variance (SOV), which characterizes the deviations of any operator from the noise-averaged operator in a stochastic evolution governed by the Hamiltonian.  Surprisingly, we find that the evolution of the noise-averaged variance relates to an out-of-time-order correlator (OTOC), which connects fluctuations of the system with scrambling, and thus allows computing the Lyapunov exponent.

[1] A. Chenu, M. Beau, J. Cao, and A. del Campo. Phys. Rev. Lett. 118:140403 (2017)
[2] L. Dupays, I. L. Egusquiza, A. del Campo,  and A. Chenu. Superadiabatic thermalization of a quantum oscillator by engineered dephasing, Phys. Rev. Res. 2:033178 (2020)
[3] L. Dupays and A. Chenu. Dynamical engineering of squeezed thermal state, Quantum 5:449 (2021)
[4] P. Martinez-Azcona, A.Kundu, A. Saxena, A. del Campo, and A. Chenu, ArXiv 2407.07746 
[5] P. Martinez-Azcona, A.Kundu, A. del Campo, and A. Chenu, Phys. Rev. Lett. 131:16202 (2023).