Talks

In this talk, we develop a systematic framework for understanding symmetries in topological phases in \(2+1\) dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon types and global symmetries permuting anyon types, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in \(2+1\) dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion \(2\)-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input UFCs that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input UFCs, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.

We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

The question of the long-time behavior of quantum trajectories has been recently solved in the finite-dimensional case. In infinite dimension, the problem is still open. In this talk, we consider the particular model of the "one-atom maser," an infinite-dimensional system with many applications in quantum mechanics. We completely describe its long-time behavior by comparing it with a classical birth-and-death process. This is a joint work with T. Benoist and L. Bruneau.

Hundred years ago Stern and Gerlach demonstrated that spin-1/2 particles moving through a very high magnetic field gradient showed spin-path entanglement. Here, we show there that one can describe the emergence of the spin state and path variable’s entanglement as a dynamical feature in Stern-Gerlach experiments using open quantum system approach. This novel approach also gives broadening of the spots on the detector as well as the collapse of the wavefunction.

Reference: 

Das, G., & Bhattacharyya, R. (2024). Irreversibility of a Stern-Gerlach experiment. Physical Review A, 110(6), 062211. (DOI: https://doi.org/10.1103/PhysRevA.110.062211)

 I will present a modification of the Sachdev-Ye-Kitaev model which demonstrates ergodicity breaking phenomenon, while retaining its' solvable structure (which is one of the signatures of the model). I will present results from various probes that detect the ergodicity breaking, and demonstrate a roadmap that will lead to a solution.

Quantum trajectory theory, also known as quantum state filtering, enables us to estimate the state of a quantum system conditioned on the measurement we perform. In cases where we measure the fluorescence from a driven two-level atom with an inefficient photo detector, the conditioned state of the atom is generally not pure, except immediately after a photon detection since then we know that the atom is in the ground state. For the detection schemes such as homodyne measurement the state is never pure since it gives rise to quantum state diffusion and not quantum state jumps. In these scenarios questions can be asked as: 
Given that I did use a photo detector and did see a particular time sequence of detections, how would the atom have behaved if instead I had chosen to measure the fluorescence using a homodyne detection scheme?
These questions are called counterfactual questions. Counterfactuality has played significant roles and has a long history in philosophy of trying to make sense of such questions. There are various approaches in how to evaluate such counterfactual questions. One such influential and attractive approach is that of David Lewis where he has a generalized analysis for counterfactuals. 

Analysis 2. A counterfactual " If it were that A, then it would be that C" is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true, but C is false. 

To evaluate our atom counterfactual problem we use his approach under the two main considerations:

1) To avoid any big, widespread, diverse violations of law. 

The antecedent of our counterfactual ( the thing that we propose to change) is our choice of measurement and that is within the laws of Quantum theory. 

2) Maximize the spatiotemporal region throughout which perfect match of particular fact prevails. 

Thus, in evaluating the counterfactual problem, any information not collected by the primary detector can be modeled as photon absorptions and should be held fixed, under the above consideration. 

Denoting these other 'clicks' , described by some list of times M, and using the actual observed record of photon-counts denoted by the list of times, N, we can calculate a conditional probability of M given N. Following this we evaluate a second conditional probability with which we are most likely to observe a homodyne record over time ,Y , if we were ( counterfactually) making a homodyne measurement given M ( since M remains fixed). Conditioning the actual state (the state conditioned on all the measurements in the counterfactual case) of the atom on these probabilities and performing an ensemble average over all possible M and Y would give us the best ( relative to trace-mean-square-deviation cost function) estimate of the counterfactual state which answers the question.