Superpositions of Quantum Gaussian Processes Enable Exact Hybrid System Dynamics and Characterisation of Gaussian-Branched Cat States

Quantum systems typically exist in definite states, but researchers continually seek to create and control superpositions, where a system exists in multiple states simultaneously. Lorenzo Braccini, Sougato Bose, and Alessio Serafini, all from the Department of Physics and Astronomy at University College London, now extend the mathematical framework for describing these superpositions to encompass more complex, hybrid systems combining continuous variables, like light fields, with discrete quantum bits. Their work introduces a new set of equations that accurately models the behaviour of these combined systems, even when interactions are complex or measurements introduce noise, without relying on approximations. This advancement enables a detailed understanding of phenomena such as entanglement generated through measurement and the creation of quantum superposition in macroscopic objects, paving the way for more sophisticated quantum technologies and fundamental tests of quantum mechanics.

The team investigates entangled states arising from specific quantum processes, naming these Gaussian-Branched Cat States. These states are fully characterised by superposed phase-space quantities, specifically sets of generalised complex first moments and covariance matrices, alongside the qubit characteristics. Researchers demonstrate this general formalism using two key examples: the measurement of qubits using a squeezed resonator, and the generation of quantum negativity in a levitated nanoparticle undergoing Stern-Gerlach interferometry.

Quantum State Evolution in Phase Space

This work provides analytical solutions for understanding how quantum states evolve in phase space, a mathematical space representing all possible states of a quantum system. Researchers derive equations describing the time evolution of key quantities, such as covariance matrices and first moments, which characterise the state of the system. These equations allow scientists to predict measurement uncertainties and accurately characterise quantum systems. The research focuses on understanding how quantum states change when subjected to various forces, decoherence, and transformations. By deriving equations that describe the time dependence of these key quantities, scientists gain insights into the behaviour of quantum systems.

The team’s approach considers the correlations between different properties of a quantum state, represented by the covariance matrix, and the average values of these properties, represented by the first moments. The team’s analysis reveals how decoherence, the loss of quantum coherence due to environmental interactions, affects the evolution of quantum states. They demonstrate that the covariance matrices decay exponentially due to decoherence, while also rotating in phase space due to interactions within the system. Furthermore, the equations show how external forces and diffusion influence the first moments, providing a comprehensive understanding of the system’s dynamics. This work provides a detailed mathematical description of how quantum states evolve in phase space under various conditions and is a valuable tool for predicting measurement uncertainties and characterising quantum systems. The focus on two specific systems, two qubits interacting with a squeezed resonator and a Stern-Gerlach interferometer, highlights the versatility and applicability of the team’s approach.

Gaussian-Branched Cat States Fully Characterised

This work extends established methods for describing continuous variable systems to encompass their interactions with qubits and qudits, resulting in a novel framework for analysing hybrid quantum systems. Researchers have developed a mathematical formalism capable of precisely modelling the behaviour of these systems, whether undergoing unitary or open dynamics, or subject to ideal or noisy measurements, without requiring approximations or truncations. This approach fully characterises the resulting states, termed Gaussian-Branched Cat States, through their phase-space properties and qubit characteristics. The team demonstrated the power of this formalism by applying it to two specific scenarios: the measurement of qubits using a squeezed resonator, and the generation of quantum negativity in a levitated nanoparticle undergoing Stern-Gerlach interferometry.

These examples highlight the method’s ability to accurately describe complex quantum phenomena in diverse physical settings. While the current work assumes Markovian noise, the authors acknowledge this is a simplification and future research could explore non-Markovian dynamics for a more complete description of open quantum systems. Further investigations could also extend the framework to analyse larger and more complex hybrid quantum systems, potentially paving the way for advancements in quantum technologies and fundamental quantum research.