Tradeoff Relation between Information and Disturbance in Quantum Measurement

Abstract

When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff relations between information and disturbance. We formulate a tradeoff relation between information and disturbance from an estimation-theoretic point of view, and derive an inequality between them. The information is defined as the classical Fisher information obtained by the measurement, and the disturbance is defined as the average loss of the quantum Fisher information. We show that pure and reversible measurements achieve the equality of the inequality. We also identify the necessary condition for various divergences between two quantum states to satisfy a similar relation. The obtained relation holds not only for the quantum relative entropy but also for the maximum quantum relative entropy.

5 pages

References in corpus (7)

• Balance between information gain and reversibility in weak measurement
• Global information balance in quantum measurements
• Information-disturbance tradeoff in estimating a maximally entangled state
• Information-Disturbance Tradeoff in Quantum State Discrimination
• Information - Disturbance Tradeoff in the Estimation of a Unitary Transformation
• Information, fidelity, and reversibility in single-qubit measurements
• Information, fidelity, and reversibility in photodetection processes

Cited by in corpus (14)

• Thermometry in the quantum regime: Recent theoretical progress
• Uncertainty and Trade-offs in Quantum Multiparameter Estimation
• Trade-off between information and disturbance in qubit thermometry
• Fundamental limits of pulsed quantum light spectroscopy: Dipole moment estimation
• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels
• Measurement disturbance and conservation laws in quantum mechanics
• Universality and Optimality in the Information-Disturbance Tradeoff
• Characterizing non-deterministic noiseless linear amplifiers at the quantum limit
• Measurement-Disturbance Tradeoff Outperforming Optimal Cloning
• Derivative of the disturbance with respect to information from quantum measurements
• Relating measurement disturbance, information and orthogonality
• Allowed region and optimal measurement for information versus disturbance in quantum measurements
• Local trade-off between information and disturbance in quantum measurements