Fisher information under decoherence in Bloch representation

Abstract

The dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit, by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $\mathfrak{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of phase parameter with the Ramsey interferometry.Comment: 16 pages, 4 figure

Electromagnetic shielding in quantum metrology

“…This kind behavior of the QFI is the same as that in the amplitude-damping channel described in [40] as expected.…”

“…On the other hand , however, interaction between a system and an environment is unavoidable in reality, and the quantum decoherence induced by such interactions may decrease the QFI and destroy the quantum entanglement in the probe system exploited to improve the precision. In this regard, It has been shown that the interaction between a system and an environment usually makes the measurements noisy, which in turn degrades the estimation precision [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Quantum Fisher information and spin squeezing in one-axis twisting model

“…In addition, decoherence processes are considered in this model. We discuss influences of the collisional dephasing [29,30,31,32] on the APEP and spin squeezing. In this case, ξ 2 K is analytically solved, while χ 2 is numerically calculated.…”

Quantum Fisher Information of Entangled Coherent States in a Lossy Mach—Zehnder Interferometer

“…Quantum Fisher information (QFI) is another significant concept in quantum metrology and has been studied widely [20,21,22,23,24,25,26,19,27,28,29]. As an extension of the classical Fisher information in statistics and information theory, QFI plays a paramount role in quantum estimation theory.…”