Entanglement Property of Tripartite GHZ State in Different Accelerating Observer Frames

Area of Science:

• Quantum Information Theory
• Quantum Entanglement
• Relativistic Quantum Information

Background:

• Uniformly accelerating reference frames in quantum field theory present unique challenges for understanding quantum phenomena.
• Minkowski states and their properties in non-inertial frames are crucial for relativistic quantum information.
• Entanglement, a key quantum resource, is susceptible to environmental influences, including acceleration.

Purpose of the Study:

• To derive analytical expressions for Minkowski states in uniformly accelerating reference frames.
• To investigate the entanglement properties of Bell and Greenberger-Horne-Zeilinger (GHZ) states in these frames.
• To quantify the impact of acceleration on quantum entanglement using negativity and von Neumann entropy.

Main Methods:

• Application of the single-mode approximation to two distinct modes.
• Analytical derivation of Minkowski states for ground and first excited states.
• Calculation of entanglement measures, including negativity and von Neumann entropy.

Main Results:

• Analytical expressions for Minkowski states in accelerating frames were obtained.
• Entanglement degree of Bell and GHZ states decreases as acceleration parameters increase.
• System stability, measured by von Neumann entropy, increases with the number of particles in the entangled system.

Conclusions:

• Quantum entanglement is sensitive to acceleration, with its degree diminishing under increasing acceleration.
• Multi-particle entangled systems exhibit enhanced stability in accelerating frames.
• The study provides insights into the behavior of quantum entanglement in non-inertial reference frames, reducing to known results in the limit of zero acceleration.