Talks

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.

We will start by discussing page-curve entanglement dynamics in freely expanding fermionic gas [1]. We will then discuss time dynamics of entanglement entropy between a filled fermionic system and an empty reservoir when there are dephasing effects [2] under various geometries.  In this context, we will employ two different kinds of quantum trajectory approaches, namely stochastic unitary unraveling and quantum state diffusion. Our findings are expected to hold for a wide variety of generic interacting quantum systems and systems subject to environmental imperfections. 

[1] M. Saha, M. Kulkarni, A. Dhar, Phys. Rev. Lett. 133, 230402 (2024)
[2] K. Ganguly, P. Gopalakrishnan, A. Naik, B. K. Agarwalla, M. Kulkarni, arXiv:2501.12110 (2025)

We present a protocol for measurement-induced transition, where at each time-step we evolve a quantum Ising chain under transverse Ising Hamiltonian for time τ, and then make a global measurement with certainty. For system size ≤28, there is a transition in entanglement at some critical value τ = τc. We also calculate survival probability of the initial state and find that some quantity derived from this probability also shows a peak at τc. Using a recurrence relation, one can compute survival probability in our set-up for size upto 1000. It is found that the critical value of τ follows a scaling τc ∝1/√N. Hence, the transition occurs for finite size only. It will be interesting to investigate the size-dependence of critical point in other measurement-induced transitions.

* Concept of an adaptive measurement and how it is distinct from feedback. 
* Applications of adaptive measurements, including quantum metrology and quantum computing.
* Applications in quantum trajectories in particular, including  
 -- "practical" applications in metrology
 -- potential applications to steering experiments (as introduced in previous lecture)
-- applications to a fundamental question: how big a brain do you need to apply quantum trajectory theory? 

Superconducting qubits have provided a fertile landscape for pioneering work examining experimental quantum trajectories. Here, continuous monitoring of a quantum system's environment can be used to unravel individual quantum trajectories of the open system evolution. Many fascinating extensions of these trajectories have been explored, including quantum state smoothing, retrodiction, parameter estimation, connections to thermodynamics, topological transitions, quantum feedback, and much more. Resisting the temptation to discuss all of these topics at breakneck pace, this talk will instead focus on a simple case: a quantum system interacting with its environment via radiative decay. This is typically and ultimately characterized by quantum jumps of the system to a lower energy level. What happens before these quantum jumps occur? Here, in the absence of quantum jumps, the dissipative interaction results in coherent, yet non-unitary evolution described by an effective non-Hermitian Hamiltonian. I will survey our recent work that explores the rich landscape of these non-Hermitian dynamics highlighting connections to quantum measurement dynamics along the way.

Multi-particle coherence and entanglement are intimately related concepts. Although due to technological advancements many thought experiments of the last century aimed at investigating coherence and entanglement can now be performed, these concepts are still far from being fully understood. Nevertheless, the efforts to understand these concepts have led to several promising quantum information technologies. One of the physical processes in which the relations between coherence and entanglement has been extensively explored is spontaneous parametric down-conversion (SPDC)—a nonlinear optical process in which a pump photon interacts with a nonlinear crystal to produce a pair of entangled photons, termed as signal and idler. Using the PDC photons, two-photon coherence and entanglement effects have been observed in several degrees of freedom including polarization, time-energy, and position-momentum. This talk will present a brief overview of interference experiments performed with SPDC photons in the last few decades for investigating two-photon coherence and entanglement. These investigations have led to several promising technologies, and this talk will discuss some of these technologies that are in the domain of quantum metrology and imaging.

* Historical overview by me of 5 independent streams leading to quantum trajectory theory. 
* My various small contributions as a PhD student when these all (more or less) came together in 1993.
* A unified description of jump and diffusion unravellings (presented by Mr Pierre Guilmin).
* My fascination with the different unravellings of simple quantum systems, and how it lead to the idea of quantum steering.
* How this would allow us to prove experimentally that there is no objective (measurement-independent) unraveling.

We introduce a time-energy uncertainty relation within the context of restarts in monitored quantum dynamics [1] . Previous studies have established that the mean recurrence time, which represents the time taken to return to the initial state, is quantized as an integer multiple of the sampling time, displaying pointwise discontinuous transitions at resonances. Our findings demonstrate that the natural utilization of the restart mechanism in laboratory experiments [2], driven by finite data collection time spans, leads to a broadening effect on the transitions of the mean recurrence time. Our proposed uncertainty relation captures the underlying essence of these phenomena, by connecting the broadening of the mean hitting time near resonances, to the intrinsic energies of the quantum system and to the fluctuations of recurrence time. Our uncertainty relation has also been validated through remote experiments conducted on an International Business Machines Corporation (IBM) quantum computer. We then discuss fractional quantizatization of the recurrence time for interacting spin systems using sub-space measurements [3].
References
[1] R. Yin, Q. Wang, S. Tornow, and E. Barkai, Restart uncertainty relation for monitored quantum dynamics Proceedings of the National Academy of Sciences 122 (1) e2402912121, (2025).
[2] R. Yin, E. Barkai Restart expedites quantum walk hitting times Phys. Rev. Lett. 130, 050802 (2023).
[3] Q. Liu, S. Tornow, D. Kessler, and E. Barkai Properties of Fractionally Quantized Recurrence Times for Interacting Spin Models arXiv:2401.09810 [condmat.stat-mech] (submitted)