Entanglement Production in Metastable State Decay Defines Entropy Increments for Separating Radiation Fragments

The fundamental process of radioactive decay inevitably creates quantum entanglement, linking the decaying atom to the emitted radiation and also between different moments in time when radiation is released. Sergei Khlebnikov from Purdue University and colleagues investigate how these two forms of entanglement interact within simplified theoretical models. The team defines specific states representing radiation emitted at different times using a mathematical technique and then calculates the increase in entanglement as radiation develops. This work establishes a new way to quantify entanglement, offering a valuable tool for understanding complex phenomena like Hawking radiation, where distinguishing between early and late-time radiation is crucial for resolving long-standing theoretical puzzles.

This research investigates the relationship between these two forms of entanglement within simplified models, offering insights into quantum decay processes. The team defines quantum states using a mathematical technique that analyzes signals over time, allowing for detailed analysis of entanglement dynamics. This approach facilitates the study of how entanglement evolves during decay and how the different forms of entanglement are interconnected, ultimately contributing to a more complete understanding of quantum phenomena in decaying systems. The work provides a framework for analysing entanglement production in a variety of physical scenarios involving unstable states and their decay products.

Scientists calculated the entanglement associated with radiation fragments emitted at different times and computed the corresponding entanglement entropy increments. Based on these results, they argue that these entropy increments serve as useful measures of entanglement, especially in scenarios, such as Hawking radiation, where it is necessary to separate the radiation into ‘old’ and ‘new’ components. Decay of an unstable state in quantum mechanics is a probabilistic process and, as such, must have an amount of entropy associated with it. This entropy reflects the uncertainty as to how much of the state has already decayed by a given time. If, for example, the decaying system starts in a pure quantum state and ends in a pure state.

Radiation Entropy Increments and Time Intervals

This research investigates the entanglement entropy (EE) associated with radiation emitted from decaying or amplifying quantum systems. Instead of focusing on the EE at a single moment, the authors define and calculate entropy increments, the EE associated with radiation emitted over finite time intervals. The core idea is to explore how these increments behave and relate to the conventional EE, particularly in scenarios relevant to information loss paradoxes like Hawking radiation. Key Findings and Concepts: * Entropy Increments: The authors propose a method to calculate the EE of radiation emitted during specific time intervals.

This differs from standard EE calculations which typically focus on a snapshot in time. * Conservation of Uncertainty: A central result is the demonstration of a relationship analogous to the standard EE property where the sum of the EE of two subsystems equals the total EE if the combined system is in a pure state. This is expressed as SB2A = SA (where SB2A is the entropy increment of the radiation (B) and the system (A), and SA is the entropy of the system A). * Behavior in Different Scenarios: The authors explore the behavior of these entropy increments in three distinct scenarios: * Decay to Vacuum: A system decaying to the vacuum state.

• Decay to a Mixed State: A system decaying to a mixed (thermal) state. * Amplification: A system undergoing parametric amplification. * Strong Subadditivity: The authors demonstrate how the strong subadditivity condition of quantum entropy (EE) can be maintained even in scenarios involving pair production (like amplification). * Relationship to Hawking Radiation: The motivation behind this work is to provide a framework for understanding the information loss paradox in Hawking radiation, where the entropy of the emitted radiation needs to be carefully tracked.

Entanglement Increments Reveal Decay Dynamics

This research establishes a refined approach to understanding entanglement within decaying systems, specifically focusing on the radiation produced during such processes. Scientists developed a method to analyze entanglement not through total entropy, but by examining ‘entropy increments’, the amount of entanglement deposited into radiation during specific time intervals. This technique proves consistent with established understandings of entanglement in simple scenarios and offers a more detailed characterization when distinguishing between radiation collected at different times, categorizing it as ‘old’ or ‘new’. By focusing on these entropy increments, researchers gain a clearer picture of how entanglement evolves during decay, offering a valuable tool for analyzing complex systems like those involved in Hawking radiation. The authors acknowledge that the precise frequency cutoff used in their calculations may influence results, but suggest that the overall trends remain consistent as long as most of the entropy is contained within a reasonable bandwidth. Future work could explore the application of this method to more complex decay scenarios and investigate the implications for understanding information loss in black hole evaporation.