Quantum Fisher Information and Lee‐Yang Zeros with Quantum Coherence of the Isotropic XY$XY$ Model and the Energy Scale

Abstract

Lee-Yang zeros lie on the complex plane of the control parameters for many-body systems with finite size, such as the transverse magnetic field and the inverse temperature. Here, an anisotropic spin system with nearest-neighbor interactions for finite-size parity space is considered. The Lee-Yang zeros are obtained in anisotropic XY model for the complex plane of the transverse magnetic field and in the isotropic XY model for the complex fugacity plane of the quantum coherence. A characteristic function to represent the probe spin coherence for the isotropic XY model, and study on Lee-Yang zeros, quantum coherence, and quantum Fisher information at the complex fugacity plane is presented. The relationship between quantum Fisher information and quantum coherence in decoherence channels is demonstrated and it is illustrated that information cannot be acquired at high temperatures. Meanwhile, the ground-state energy on the complex plane for the anisotropic XY model is studied and the free energy cumulants with the partition function of the anisotropic XY model for parity space is calculated.

Quantum Parameter Estimation With Graph States In SU(N) Dynamics

“…Among these resources, quantum entanglement states play a significant role in quantum metrology, as they can be employed to address various quantum metrology problems, including the mapping of magnetic fields, [29][30][31][32][33] phase imaging, [34][35][36][37][38][39][40] and global frequency standards. [41] Moreover, they have been extensively studied both theoretically and experimentally in the context of quantum speed limit, [42,43] Lee-Yang zeros, [44,45] and quantum multiparameter parameter estimation. [16,[46][47][48][49][50][51][52][53][54] The ultimate precision limit in parameter estimation is given by the quantum Cramér-Rao bound.…”

Nonequilibrium Effects on the Precision of Parameter Estimation

“…Improving the precision of parameter estimation is a significant issue in modern quantum metrology, [1][2][3][4] in which quantum Fisher information (QFI) is fundamental and provides the lower bound to the estimation precision in terms of quantum Cramér-Rao bound (QCRB). Recently, QFI has been studied from various perspectives due to its versatile applications in many branches of physics, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] such as non-Markovianity, [7,8] Gaussian processes, [10,11] quantum speed limit, [13,14] and quantum correlations. [15][16][17][18][19][20] Furthermore, detecting gravitational waves, biological imaging, and many other highlevel applications involve unknown parameters, ranging from sensing magnetic, electric, and gravitational fields to clock synchronization protocols.…”