Talks

We consider the problem of quantum error correction (QEC) for non-Markovian noise. We show that conditions for approximate QEC can be easily generalized for the case of non-Markovian noise, in the strong coupling regime where the noise map becomes non-completely-positive at intermediate times. While certain adaptive recovery schemes are ineffective against quantum non-Markovian noise, in the sense that the fidelity vanishes in finite time, a specific strategy based on the Petz map uniquely safeguards the code space even at the maximum noise limit. Focusing on the case of non-Markovian amplitude damping noise, we observe that the non-Markovian Petz map also outperforms the standard, stabilizer-based QEC code. Since implementing such a non-Markovian map poses practical challenges, we also construct a Markovian Petz map that achieves similar performance, with only a slight compromise on the fidelity.
[Based on arXiv:2411.09637]

The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Such a framework has been developed during the last decade, with recent advances incorporating multiple conserved quantities, the assessment of thermodynamic quantities at stopping times using martingale theory, and the consideration of imperfect and partial monitoring schemes. These advances provide new universal relations in the form of fluctuation theorems and inequalities that refine our understanding of the second-law of thermodynamics in different senses.

Structure of dynamical models describing  open quantum systems including measurement back-action and decoherence: discrete-time models based on quantum channels and  left stochastic matrices;  continuous-time  models driven by Wiener processes (weak measurement) and Poisson processes (quantum jump and counting measurement).

Quantum theory contravenes classical macrorealism by allowing a system to be in a superposition of two or more physically distinct states, producing physical consequences radically different from that of classical physics. Motivated by this, we construct superpositions between time evolution unitaries and study the dynamics of a qubit under such superposed unitary operators. We find that the superposition of unitaries significantly affects the trajectory of the qubit in the Bloch sphere by shifting the path of evolution and making the speed of evolution non-linear in time. The qubit spends more time near the poles of the Bloch sphere and passes through the equator rather quickly. This  remarkably enhances the endurance against dephasing noise, making the superposed unitaries suitable for robust quantum control tasks. Moreover, we observe an extreme violation of Leggett-Garg inequalities beyond the temporal Tsirelson's bound, which increases with increasing superposition between the unitaries. This shows stronger temporal correlations achieved by the superposed unitares. Using an NMR quantum register, we experimentally demonstrate the superposition of unitaries with the help of an ancillary qubit and verify our theoretical predictions.

Quantum walks, the quantum analogs of classical random walks, have become powerful tools in quantum information processing, offering unique advantages in areas such as quantum computation, search algorithms, and quantum transport. While homogeneous quantum walks with uniform coin operations have been well studied, introducing inhomogeneity - by varying the coin operator or evolution across time and space opens new avenues for controlling the dynamics and properties of quantum systems. Our research has explored the impact of such inhomogeneous quantum walks, yielding two significant results. First, we demonstrated Parrondo's paradox in discrete-time quantum walks using space- and time-dependent coins, achieving paradoxical outcomes without requiring higher-dimensional coins or decoherence, thus enhancing the practicality of implementations [1]. Second, by introducing a Gaussian-profiled coin rotation angle, we showed that this configuration not only improves localization of the walker's probability distribution but also generates maximal entanglement rapidly and a correlation that is robust against decoherence [2]. These findings underscore the potential of inhomogeneous quantum walks for more efficient and resilient quantum technologies.

Control and manipulation of quantum states by measurements and bath engineering in open quantum systems, and associated phenomena, such as measurement-induced phase transitions, have emerged as new paradigms in many-body physics. Here, taking a prototypical example of Josephson junction arrays (JJAs), I will discuss how repetitive monitoring can transform an insulating state in these systems to a superconductor and vice versa. To this end, we study the effects of continuous weak measurements and feedback control on isolated JJAs in the absence of any external thermal bath. The monitoring due to combined effect of measurements and feedback, inducing non-unitary evolution and dissipation, leads to a long-time steady state characterized by an effective temperature in a suitably defined semiclassical limit. However, we show that the quantum dissipation due to monitoring has fundamental differences with equilibrium quantum and/or thermal dissipation in the well-studied case of JJAs in contact with an Ohmic bath. In particular, using a variational approximation, and by considering the semiclassical, strong measurement/feedback and weak-coupling limits, we demonstrate that this difference can give rise to re-entrant steady-state phase transitions, resulting in transition from an effective low-temperature insulating normal state to superconducting state at intermediate temperature. Our work emphasizes the role of quantum feedback, that acts as an additional knob to control the effective temperature of non-equilibrium steady state leading to a phase diagram, not explored in earlier works on monitored and open quantum systems.

We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with an instantaneous reset to a specified set of reset configurations taking place with a probability that depends on the current configuration of the system at the instant of reset? Analyzing the protocol in the framework of the so-called tight-binding model describing the hopping of a quantum particle to nearest-neighbor sites in a one-dimensional open lattice, we obtain analytical results for the probability of finding the particle on the different sites of the lattice. We explore a variety of dynamical scenarios, including the one in which the resetting time intervals are sampled from an exponential as well as from a power-law distribution. Under exponential resetting, the system relaxes to a stationary state characterized by localization of the particle around the reset sites. The choice of the reset sites plays a defining role in dictating the relative probability of finding the particle at the reset sites as well as in determining the overall spatial profile of the site-occupation probability. Furthermore, analyzing the case of power-law resetting serves to demonstrate that the attainment of the stationary state in this quantum problem is not always evident and depends crucially on whether the distribution of reset time intervals has a finite or an infinite mean. 

There is more matter than antimatter in the universe. This asymmetry requires three conditions: 1- Baryon (or lepton) number violation, 2- C and CP violation and 3- out-of-thermal equilibrium conditions in the early universe, before BBN. Although the SM does not have any out-of-equilibrium process, it does provide baryon number violation and CP violation. Still, it is commonly accepted that the SM CP violation is not enough for producing the observed baryon asymmetry. I will present one new physics model in which the SM CP violation, that is measured in the B meson system, is in fact enough to generate the baryon asymmetry. 

The 21-cm line from neutral hydrogen holds immense potential as a probe of early astrophysics and cosmic evolution. Realizing the potential of this observational probe, however, is limited by our ability to control systematic effects in the data and model the cosmological 21-cm signal. In this talk, I will provide an overview of the observational prospects made possible through the cosmic 21-cm signal and discuss the challenges confronting interferometric experiments that are targeting a high-redshift detection. I will focus on recent developments from the Hydrogen Epoch of Reionization Array (HERA), covering our latest upper limits on the 21-cm power spectrum and their implications for early X-ray heating of the intergalactic medium. I will additionally discuss our latest efforts to understand and mitigate mutual coupling, a complex systematic effect in the data that threatens to thwart our efforts to detect the cosmological 21-cm signal. I will conclude by discussing the path forward with HERA, with a preliminary view of what to expect from forthcoming analyses.