Quantum Coherence Measures in Entangled Atomic Systems Decay with Increased Gaussian Wave Packet Width

The fundamental nature of quantum coherence, a key ingredient for many quantum technologies, faces challenges when considering systems in motion, particularly at relativistic speeds. Arnab Mukherjee, Soham Sen, and Sunandan Gangopadhyay investigate how the principles of special relativity, specifically Lorentz transformations, impact the measurement of coherence within entangled atomic systems. Their work explores how an observer’s motion affects the perceived coherence of two entangled particles, considering scenarios where one or both particles experience a relativistic boost. The results demonstrate a general decay of coherence with increasing particle separation, boost velocity, and the number of particles undergoing relativistic motion, offering crucial insights for maintaining coherence in future quantum devices operating in dynamic environments.

Relativistic Entanglement and Lorentz Transformations

This research explores how quantum entanglement, a fundamental connection between particles, is affected by the principles of special relativity, specifically Lorentz transformations. These transformations describe how measurements of space and time change when viewed from different moving frames of reference. The study investigates what happens to entanglement when particles are accelerated to relativistic speeds, approaching the speed of light. Quantum entanglement links particles so they share the same fate, regardless of distance; measuring a property of one instantly reveals information about the other, a cornerstone of emerging quantum technologies.

Researchers focused on Gaussian wave packets, a mathematically convenient way to model quantum particles, and examined scenarios with narrow uncertainty, meaning a precise knowledge of certain particle properties. The team discovered that, under specific conditions, quantum coherence is preserved even when particles undergo a Lorentz boost. Maintaining coherence is crucial for building practical quantum computers and communication systems. This work has implications for long-distance quantum communication and robust quantum computing. By developing new mathematical tools for quantifying coherence, scientists are pushing the boundaries of what’s possible in quantum technology. This contributes to a deeper understanding of the interplay between quantum mechanics and special relativity, potentially revealing fundamental laws of nature and advancing the field of quantum information theory.

Lorentz Boosts Preserve Quantum Coherence

This research investigates how relativistic effects, specifically Lorentz transformations, impact quantum coherence in entangled systems. Scientists examined two scenarios involving entangled pairs of particles, considering cases where the boost affects one particle or both particles within the pair. The team calculated the resulting quantum states after applying these boosts and then quantified the degree of coherence using two distinct measures, the l1-norm and the Frobenius-norm, with a focus on narrow Gaussian wave packets. Results demonstrate that the l1-norm measure of coherence remains largely unaffected by the Lorentz boost in both scenarios and exhibits consistency regardless of the Gaussian wave packet width.

However, the Frobenius-norm measure reveals a more nuanced picture. When the boost is applied to a single particle, coherence loss becomes more pronounced with wider wave packets and higher boost parameters. Significantly, when both particles experience the boost, coherence degrades much more rapidly, particularly at larger wave packet widths and high boost values. This suggests that the combined effect of relativistic boosts on entangled particles leads to a substantial reduction in quantum coherence. This study provides valuable insight into the interplay between relativistic effects and quantum coherence, contributing to a deeper understanding of quantum systems in extreme conditions.

Relativistic Quantum State Transformations and Entanglement

This study investigates how Lorentz transformations, representing relativistic motion, impact the coherence of quantum systems, both single particles and entangled pairs. Scientists began by defining the initial quantum state of a particle, considering its momentum and spin, and then applied a Lorentz boost using a specific transformation equation. This equation incorporates the particle’s four-momentum and utilizes a rotation matrix, effectively describing how the quantum state evolves under relativistic motion. The transformation involves a connection between spin and momentum, termed spin-momentum entanglement.

To model the effects of a boost, scientists calculated the transformed density matrix, a mathematical tool describing the probability distribution of quantum states, by considering the momentum of the particle. This allowed them to determine how coherence changes after the Lorentz transformation. The team then extended this analysis to a system of two entangled particles, examining scenarios where one or both particles experience the boost. They calculated the transformed quantum state and density matrix for both cases, integrating over momentum space and utilizing the properties of the density matrix to determine the effects of the boost on entanglement. The resulting expressions reveal how coherence and entanglement are affected by relativistic motion, providing insights into the fundamental interplay between quantum mechanics and special relativity.

Relativistic Boosts Diminish Atomic Coherence

This research delivers a detailed investigation into how Lorentz transformations impact the coherence of two-particle atomic systems, precisely measuring coherence decay under relativistic boosts. Scientists comprehensively analyzed coherence as measured by an observer in motion, meticulously examining the influence of boost parameters and the width of the Gaussian wave packets used to model the particles. The study considered two scenarios: a single particle undergoing a relativistic boost while the other remains stationary, and both particles simultaneously experiencing boosts. Measurements confirm that coherence demonstrably decays with increasing wave packet width, higher boost parameters, and a greater number of particles subjected to the boost.

The team mathematically formulated this decay, deriving expressions for the reduced density matrix of the two-particle system under various boost conditions. Specifically, they obtained the reduced density matrix for the case where one particle is boosted, revealing a clear relationship between coherence and the boost. This research provides a rigorous mathematical description of coherence loss under relativistic conditions, offering valuable insights for quantum information processing and relativistic quantum optics.