Quantum Fisher information matrix in Heisenberg XY model

Abstract

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cramér-Rao bound. In this work, we study simultaneous and individual estimation strategies using the density matrix vectorization method. Two special Heisenberg XY models are considered. The first one concerns the anisotropic XY model in which the temperature T and the anisotropic parameter γ are estimated. The second situation concerns the isotropic XY model submitted to an external magnetic field B in which the temperature and the magnetic field are estimated. Our results show that the simultaneous strategy of multiple parameters is always advantageous and can provide a better precision than the individual strategy in the multiparameter estimation procedures.

Ultimate precision of joint parameter estimation under noisy Gaussian environment

“…The different QCRBs can be obtained from the QFIM [29,66,67], which plays an important role in multiparameter quantum metrology. It provides the appropriate tool to get the precision limits for estimating simultaneously several parameters.…”

Multiparameter quantum critical metrology

“…Quantum metrology exploits quantum effects to enhance the sensitivity in the estimation, providing advantages in a variety of applications which ranges from gravitational wave detection [3], measuring standards, magnetometry [4], thermometry, imaging [5,6], navigation, remote sensing, super-resolution [7][8][9][10] and many more [11]. Most of these applications intrinsically involve the estimation of multiple parameters at the same time, which explains the growing interest in multiparameter quantum metrology [12][13][14], both theoretically and experimentally [43][44][45][46][47]. The extreme sensitivity to small parameter changes is one of the defining characteristic of quantum many-body systems near criticality [48,49].…”

Revealing Trade off Relations Among Thermal Coherences and Correlations in Heisenberg XXX Model Under Inhomogeneous Magnetic Eld

“…In search of nding universal resource quantier for quantum correlation and coherence, the theorists have proposed many quantiers, such as quantum Fisher information (QFI) [12], quantum discord (QD) [2], quantum coherence [1], quantum concurrence [8], rst-order coherence (FOC) [13], Shannon-Jenson divergence coherence (SJDC) [14], and many more. The superiority of one quantier over others in capturing quantum correlations and quantum coherence and their applicability, attracts researchers to investigate the dynamics of these quantiers in dierent existing quantum mechanical systems, such as spin chains [15][16][17][18][19][20], optomechanics [21], quantum dots [22][23] and many other quantum states. These investigations are of great importance as they help us retrieve the quantum properties of a system and act as a tool for nding the universal quantum correlation and coherence quantier.…”