Entanglement detection via subsystem quantum Fisher information

Long-Mei Yang, Bao-Zhi Sun, Bin Chen +2 more

Ao-Xiang Liu, Ma-Cheng Yang, Cong‐Feng Qiao

Florent Ferro, Maurizio Fagotti

Quantum Fisher Information (QFI) is a ubiquitous quantity with applications ranging from quantum metrology and resource theories to condensed matter physics. In equilibrium local quantum many-body systems, the QFI of a subsystem with respect to an extensive observable is typically proportional to the subsystem's volume. Specifically, in large subsystems at equilibrium, the QFI per unit volume squared becomes negligible. We reveal a natural mechanism that amplifies the QFI in a quantum spin chain with a zero-temperature ordered phase. At zero or sufficiently low temperatures, a transient localized perturbation enhances the QFI, causing it to scale quadratically with the subsystem's length. Furthermore, this enhancement can be controlled through more general localized kicking protocols. We also revisit the behavior of the quantum Fisher information after a global quench in the thermodynamic limit, focusing on the generation of localized -- confined within compact subsystems -- multipartite entanglement. We show that the density of localized multipartite entanglement approaches zero at late times, but there is an optimal time frame proportional to the length in which subsystems fall into macroscopic quantum states. We test our predictions against numerical data obtained using a novel technique, based on a remarkable identity between quantum Fisher information and Wigner-Yanase-Dyson skew information, that allows one to compute the quantum Fisher information with respect to the order parameter in noninteracting spin chains.

Nan Li, Shunlong Luo

We propose an entanglement criterion in terms of quantum Fisher information, which complements the criterion based on variance and local uncertainty relations [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. We illustrate the significance of this criterion by showing that it can reveal entanglement undetectable by the variance method. The dual relation between the criterion based on quantum Fisher information and that based on variance are highlighted. The combination of these two criteria leads to a refined method for entanglement detection, which is stronger than when either one is used alone.

A.‐S. F. Obada, S. Abdel‐Khalek

Y. Akbari-Kourbolagh, M. Azhdargalam

We propose a sufficient entanglement criterion for the multipartite systems based on quantum Fisher information. It complements the well-established positive partial transpose criterion in the sense that it is also able to detect bound entangled states. Moreover, it improves the well-known upper bound on the quantum Fisher information of separable multiqudit states introduced by Toth et al. [G. Toth and T. Vertesi, Phys. Rev. Lett. 120, 020506 (2018)] and hence detects a greater number of metrologically useful entangled states. This criterion is formulated as a simple inequality which must be fulfilled by the quantum Fisher information of separable states of multipartite systems. Violation of this inequality by a state reveals its entanglement and accordingly confirms its usefulness for quantum metrology. The efficiency of this criterion for detection of entanglement is illustrated through some examples.