Tag - Theoretical computer science

The steady states of Markovian processes can be written as extremal eigenvectors of a matrix (e.g., a quantum channel) that generates the dynamics. Unlike ground states of Hamiltonians, however, the gap of the channel does not necessarily control relaxation to the ground state. I will argue that this discrepancy is precisely what allows non-trivial gapped phases of Lindbladians to exist. I will discuss an alternative criterion for deciding whether two Lindbladians (and their steady states) are in the same phase. I will show that this criterion implies many of the properties one would naturally demand of a phase, such as the persistence of any long-range order and the analytic evolution of correlation functions within a phase.

Multi-photon states can play an important role for optical quantum information, but producing these effectively can be challenging. Most commonly, independent photon pairs are produced by downconversion and then combined probabilistically, using post-selection to obtain the desired multi-photon state. This dependence on post-selection limits the suitability of the resulting states for some application. An alternative approach is to use cascaded downconversion: by sending photons produced with downconversion into a second non-linear crystal to be downconverted again, it is possible to produce photon triplets directly. In this talk, I will present work from my group and others exploring this novel process and discuss current research directions aiming to make cascaded downconversion more useful for state generation and beyond.

Thousands of papers have been written about quantum metrology, but few have acknowledged the reality that quantum sensors such as gravitational-wave detectors are dynamical systems and the signals are often time-varying. This talk presents fundamental quantum limits to such sensors, as well as measurements to achieve them. For the task of noise spectroscopy with an optical interferometer, I show the surprising result that spectral photon counting can be far superior to homodyne detection. This idea has recently been adopted by Caltech scientists, who will build an experiment based on the idea to detect signatures of quantum gravity under the GQuEST project.

High-dimensional quantum states are desirable for the study of complex quantum systems and the development of quantum technologies. Yet, their implementation can be challenging as it is their characterization. In the first part of this talk, I will focus on recent progress in the generation of high-dimensional quantum states in photonic circuits. I will show how this approach can make the implementation of large quantum states flexible and scalable by exploiting the intrinsic advantages of integrated devices. In the second part of the talk, I will deal with the more general problem of characterizing large quantum systems. Specifically, I will present some recent results on the study of multi-qubit systems by means of threshold quantum state tomography, an approach that can significantly reduce the number of measurements necessary to reconstruct the whole state density matrix.

The conditional expectation is an essential concept in probability theory and a basic tool in Bayesian estimation, as it allows one to infer hidden variables from observations in an optimal sense. Many have tried to generalize the concept for quantum mechanics, but the literature on the subject remains fragmented, confusing, and controversial. This talk presents a formalism of generalized conditional expectations that unifies most of the previous approaches. I also show how a certain version of the generalized conditional expectation can be useful for the study of quantum estimation. For example, it leads to a quantum Rao-Blackwell theorem, which may be used to improve the design of a quantum sensor in the same way the classical theorem can improve an estimator.