Talks

* 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)

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 this talk, I will discuss how one can use the gravitational path integral to compute the supersymmetric index of black holes as well as other black objects in string theory. The saddles that I shall describe admit a non-zero temperature, consequently lacking an infinitely long AdS throat that separates the horizon from the asymptotic region, and also admit periodic boundary conditions for fermionic fields around the thermal circle, consequently counting bosonic and fermionic states with an opposite sign. Since the microscopic calculation of these indices is oftentimes well understood yet the saddles that I shall describe now lack the conventional decoupling limit taken in AdS/CFT, our analysis represents a first step towards understanding holography for supersymmetric observables in flat space.