A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels

TL;DR

This paper derives analytical formulas for quantum Fisher and Skew information for two-qubit X-states, compares them for specific states, and studies their dynamics under various decoherence channels, revealing similar behaviors.

Contribution

It provides the first analytical expressions for these informational quantities for arbitrary two-qubit X-states and analyzes their decoherence dynamics, highlighting their similar roles in quantum estimation.

Findings

Analytical formulas for quantum Fisher and Skew information for two-qubit X-states.

Decoherence significantly affects these quantum informational quantities.

Quantum Fisher and Skew information exhibit similar dynamic behaviors under decoherence.

Abstract

In statistical estimation theory, it has been shown previously that the Wigner-Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cram\'er-Rao inequality is expressed in terms of skew information. Since these two fundamental quantities are based on the concept of quantum uncertainty, we derive here their analytical formulas for arbitrary two qubit $X$-states using the same analytical procedures. A comparison of these two informational quantifiers for two quasi-Werner states composed of two bipartite superposed coherent states is examined. Moreover, we investigated the decoherence effects on such quantities generated by the phase damping, depolarization and amplitude damping channels. We showed that decoherence strongly influences the quantum criteria during the evolution and these quantities exhibit similar dynamic behaviors. This current work is characterized by the fact that these two concepts play the same role and capture similar properties in quantum estimation protocols.