A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg $XY$ model

Abstract

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in the multi-component quantum system [S. Kim et al., Phys. Rev. A. 97, 032326 (2018)]. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg $XY$ model. Two distinct situations are considered. The first one concerns the anisotropic $XY$ model and the second situation concerns the isotropic $XY$ model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.

16 pages, 8 figures

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• Effects of DM and KSEA interactions on entanglement, Fisher and Wigner-Yanase information correlations of two XYZ-Heisenberg-qubit states under a magnetic field
• A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels
• Thermal local quantum uncertainty in a two-qubit-superconducting system under decoherence
• A comparative study of LQU and LQFI in general qubit-qutrit axially symmetric states
• Robust quantum entanglement and teleportation in the tetrapartite spin-1/2 square clusters: Theoretical study on the effect of a cyclic four-spin exchange
• Quantifying non-Markovianity via local quantum Fisher information
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• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• Local quantum Fisher information and one-way quantum deficit in spin-$\frac{1}{2}$ $XX$ Heisenberg chain with three-spin interaction
• Cleaner Production in Optimized Multivariate Networks: Operations Management through a Roll of Dice
• Coherence and Entanglement in a Non-commutative Spacetime