Effect of relativistic acceleration on localized two-mode Gaussian quantum states

Abstract

We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen proper accelerations of the observers and independently tuned distance between them. To do so, we introduce a generalized Rindler frame of reference and analytically derive the corresponding state transformation as a Gaussian channel. Our approach provides several new insights into the phenomenon of vacuum entanglement such as the highly non-trivial effect of spatial separation between the observers including sudden death of entanglement. We also calculate the fidelity of the two-mode channel for non-vacuum Gaussian states and obtain bounds on classical and quantum capacities of a single-mode channel. Our framework can be directly applied to any continuous variable quantum information protocol in which the effects of acceleration or gravity cannot be neglected.

21 pages, 13 figures. A few typos corrected

References in corpus (8)

• Sudden Death of Entanglement
• The Unruh effect and its applications
• Direct and Reverse Secret-Key Capacities of a Quantum Channel
• Relativistic Quantum Teleportation with Superconducting Circuits
• Entanglement and discord: accelerated observations of local and global modes
• Quantum error correction may delay, but also cause, entanglement sudden death
• On the classical capacity of quantum Gaussian channels
• Quantum accelerometer: distinguishing inertial Bob from his accelerated twin Rob by a local measurement

Cited by in corpus (17)

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• Effect of acceleration on localized fermionic Gaussian states: from vacuum entanglement to maximally entangled states
• Entanglement extracted from vacuum into accelerated Unruh-DeWitt detectors and energy conservation
• Effect of relativistic acceleration on continuous variable quantum teleportation and dense coding
• Satellite-based quantum steering under the influence of spacetime curvature of the Earth
• Quantumness near a Schwarzschild black hole
• Monogamy of Einstein-Podolsky-Rosen steering in the background of an asymptotically flat black hole
• Relativistic (2,3)-threshold quantum secret sharing
• Effects of gravity on quantum key distribution
• Tripartite measurement uncertainty in Schwarzschild space-time
• Massive Unruh particles cannot be directly observed
• Multimode theory of Gaussian states in uniformly accelerated frames
• Generalized thermalization for integrable system under quantum quench
• Collective dynamics of accelerated atoms
• Two-mode Gaussian quantum states measured by collinearly and noncollinearly accelerating observers
• Effect of relativistic motion on witnessing non-classicality of quantum states
• Impact of the Unruh effect on the estimation precision of Gaussian channel parameters