Entropic uncertainty relations under the relativistic motion

Abstract

The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). In this Letter, we explore how the relativistic motion of the system would affect the EUR in two sample scenarios. First, we show that the Unruh effect of an accelerating particle would surely increase the uncertainty if the system and particle entangled initially. On the other hand, the entanglement could be generated from nonuniform motion once the Unruh decoherence is prevented by utilizing the cavity. We show that, in a uncertainty game between an inertial cavity and a nonuniformly accelerated one, the uncertainty evolves periodically with respect to the duration of acceleration segment. Therefore, with properly chosen cavity parameters, the uncertainty bound could be protected. Implications of our results for gravitation are also discussed.

7 pages, 3 figures

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• Improving the bidirectional steerability between two accelerated partners via filtering process
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• Quantum Fisher information as a probe for Unruh thermality
• Entanglement Enhanced Thermometry in the Detection of the Unruh Effect
• Bell inequalities violation within non-Bunch-Davies states
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
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• Multiple uncertainty relation for accelerated quantum information
• Thermality of the Unruh effect with intermediate statistics
• Experimental testing of entropic uncertainty relations with multiple measurements in pure diamond
• The dynamics of entropy uncertainty for qutrit system under the random telegraph noise