Fisher Information of a Black Hole Spacetime

Abstract

Relativistic quantum metrology is the study of optimal measurement procedures within systems that have both quantum and relativistic components. Here we use Unruh-DeWitt detectors coupled to a massless scalar field as probes of thermal parameters in different spacetimes via a relativistic quantum metrology analysis. We consider both (2+1)-dimensional anti-de Sitter and BTZ black hole spacetimes. We compute the Fisher information to identify characteristics of the black hole spacetime and to compare it to a uniformly accelerating detector in anti-de Sitter space. We find the dependence of the Fisher information on temperature, detector energy gap, black hole mass, interaction time, and the initial state of the detector. We identify strategies that maximize the Fisher information and therefore the precision of estimation.

23 pages, 8 figures

References in corpus (9)

• Optimal quantum estimation of the Unruh-Hawking effect
• Quantum estimation of the Schwarzschild space-time parameters of the Earth
• Relativistic Quantum Metrology in Open System Dynamics
• Non-Markovian time evolution of an accelerated qubit
• Quantum imprints of gravitational shockwaves
• Effective master equations for two accelerated qubits
• Entanglement Harvesting with a Twist
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• Gravitational time dilation as a resource in quantum sensing

Cited by in corpus (9)

• Dissipative dynamics of an open quantum battery in the BTZ spacetime
• Direct Characteristic-Function Tomography of the Quantum States of Quantum Fields
• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution
• Reliable quantum master equation of the Unruh-DeWitt detector
• Relative entropy formulation of thermalization process in a Schwarzschild spacetime
• Memory Effects and Entanglement Dynamics of Finite time Acceleration
• Quantum Parameter Estimation for Detectors in Constantly Accelerated Motion
• Thermal Fisher information for a rotating BTZ black hole