Tomographic Measurements Demonstrate Decoherence and Emergence of Classicality in Quantum Systems

The fundamental process of decoherence, where quantum systems lose their coherence and begin to behave classically, receives detailed examination in new work by Dorje C. Brody of the University of Surrey and Rishindra Melanathuru of Imperial College London. This research investigates decoherence arising not from direct observation of a system’s properties, but from environmental monitoring of its overall state, and demonstrates how this process fundamentally alters quantum probability distributions. The team reveals that environmental monitoring forces these distributions to become manifestly positive, effectively modelling the emergence of classical behaviour, and importantly, shows that larger quantum systems decohere at an accelerated rate. This understanding of decoherence provides crucial insight into the transition between the quantum and classical worlds, and advances our ability to model complex quantum systems.

Researchers perform real-space tomographic measurements using mathematical tools that describe the evolution of quantum systems, and its continuous time unravelling from established equations governing quantum dynamics. The effect of decoherence, the loss of quantum properties, is analysed by studying the evolution of quasiprobability distributions on the state-space of the system. Results show that decoherence renders an arbitrary quasiprobability distribution manifestly positive, thus modelling the emergence of classicality. The decoherence timescale, the minimum time that quasiprobability distributions of every initial state of the system become nonnegative, decreases in Hilbert-space dimension, and hence larger quantum systems decohere faster.

Visualising Quantum States with Quasiprobabilities

This research explores the fundamental concepts of decoherence and quasiprobability distributions, providing insights into the transition from quantum to classical behaviour. Decoherence is the process by which quantum systems lose their unique quantum properties, such as superposition and entanglement, and begin to behave more classically due to interaction with their environment. Quasiprobability distributions are mathematical functions that attempt to represent quantum states in a way that resembles classical probability distributions, allowing scientists to visualise and analyse quantum states using familiar concepts. Examples of these distributions include the Wigner function, Husimi Q function, and Sudarshan distributions.

This work focuses on universal decoherence, the idea that any quantum system will lose its quantum properties if it interacts with a sufficiently complex environment, regardless of the specific details of that environment. The research utilizes the concept of phase space, a mathematical space representing all possible states of a system, and employs tomography, the process of reconstructing the quantum state of a system from a series of measurements. This paper investigates how universal decoherence affects quasiprobability distributions, developing a model to understand how a quantum system loses its quantum properties when interacting with a generic environment. The key findings demonstrate that both discrete and continuous models accurately describe the process.

A central result is that continuous-time universal decoherence shifts the order parameter of a quasiprobability distribution linearly with time, indicating a loss of quantumness. The researchers also derived a formula for the decoherence timescale, revealing that it decreases as the size of the quantum system increases, meaning larger systems decohere faster. Furthermore, the analysis of the minimum value of the quasiprobability distribution shows how it changes with time and system size, eventually becoming non-negative as the system decoheres. These findings provide a deeper understanding of the quantum-to-classical transition and support the idea that decoherence is a fundamental process.

This work provides insights into understanding the quantum-to-classical transition, explaining why we don’t observe quantum effects in everyday macroscopic objects. The model supports the idea that decoherence is a fundamental process that happens regardless of the specific environment. The finding that larger systems decohere faster is counterintuitive but important, suggesting that the decoherence process might be more efficient in complex systems.

Environmental Monitoring Drives Quantum Decoherence

Scientists have demonstrated a novel model of decoherence, a process where quantum systems lose their unique properties and begin to resemble classical systems, by focusing on environmental monitoring of a system’s state rather than monitoring a specific observable. The work establishes a detailed understanding of decoherence using two equivalent formulations, one based on repeated measurements and the other on a continuous-time model derived from established equations governing quantum dynamics. Researchers analysed the evolution of quasiprobability distributions to characterise this decoherence effect, revealing that it effectively forces an arbitrary quasiprobability distribution to become manifestly positive, thereby modelling the emergence of classicality. Experiments show that the timescale for decoherence decreases as the Hilbert-space dimension, essentially the size of the quantum system, increases, meaning larger quantum systems decohere more rapidly.

The team defined the decoherence timescale as the minimum time required for quasiprobability distributions of any initial state to become nonnegative, and found this timescale decays in proportion to the inverse of the system size multiplied by the logarithm of the system size for large systems. This implies that macroscopic quantum systems will virtually instantly lose the negativity of any quasiprobability distribution under this tomographic decoherence model. The research involved modelling decoherence using a universal state-space tomographic measurement, where the outcome is the position of the system’s state in a mathematical space describing its properties. Analysis of the density matrix, a mathematical object describing the quantum state, revealed that for a quasiprobability distribution of degree σ, negativity disappears when the number of measurements exceeds a certain threshold. Furthermore, the continuous-time model, derived using established equations, accurately interpolates the outcomes of the discrete measurements, providing a consistent framework for understanding the decoherence process. These findings establish a precise timescale for the loss of quantum properties and offer new insights into the transition from quantum to classical behaviour.

Decoherence Timescale and System Size Relationship

This research details a comprehensive analysis of decoherence, the process by which quantum systems lose their unique quantum properties and begin to resemble classical systems. Scientists developed a universal model of decoherence, examining how environmental interactions cause this transition using both discrete and continuous mathematical frameworks. The team demonstrated that decoherence can be understood by tracking the evolution of quasiprobability distributions, which effectively show how quantum states transform into classical probabilities. Importantly, the study reveals that larger quantum systems decohere more rapidly than smaller ones, establishing a clear relationship between system size and the speed of classicalization. The researchers identified a ‘decoherence timescale’, a minimum time after which quasiprobability distributions become non-negative, signifying the emergence of classical behaviour for any initial quantum state. While the model offers a robust theoretical framework, the authors acknowledge the experimental challenge of creating a truly ‘universal’ environment that does not favour specific measurements, a factor that complicates direct verification.