Dynamic Evolution of Quantum Fisher and Skew Information under Decoherence in Three-Qubit X-States

TL;DR

This paper derives analytical formulas for quantum Fisher and skew information in three-qubit X-states and studies their evolution under various decoherence channels, revealing how noise affects quantum measurement precision.

Contribution

It provides the first closed-form expressions for QFI and SQI in three-qubit X-states under decoherence, linking these metrics to entanglement measures.

Findings

Phase damping and phase-flip channels better preserve measurement precision.

Decoherence generally reduces quantum Fisher and skew information.

Comparison with concurrence shows decoherence impacts metrological usefulness.

Abstract

Quantum metrology leverages quantum effects such as squeezing, entanglement, and other quantum correlations to boost precision in parameter estimation by saturating quantum Cramer Rao bound, which can be achieved by optimizing quantum Fisher information or Wigner-Yanase skew information. This work provides analytical expressions for quantum Fisher and skew information in a general three-qubit X-state and examines their evolution under phase damping, depolarization, and phase-flip decoherence channels. To illustrate the validity of our method, we investigate their dynamics for a three-qubit Greenberger-Horne-Zeilinger (GHZ) state subjected to various memoryless decoherence channels. Closed-form expressions for QFI and SQI are derived for each channel. By comparing these metrics with the entanglement measure of concurrence, we demonstrate the impact of decoherence on measurement precision for quantum metrology. Our results indicate that phase damping and phase-flip channels generally allow for better parameter estimation compared to depolarization. This study provides insights into the optimal selection of noise channels for enhancing precision in quantum metrological tasks involving multi-qubit entangled states.