Abstract
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. However the effects on the entanglement dynamics such as decoherence usually decrease the QFI considerably. On the other hand, Dzyaloshinskii-Moriya (DM) interaction has been shown to excite entanglement. Since an increase in entanglement does not imply an increase in QFI, and also there are cases where QFI decreases as entanglement increases, it is interesting to study the influence of DM interaction on quantum metrology. In this work, we study the QFI of thermal entanglement of two-qubit and three-qubit Heisenberg models with respect to SU(2) rotations. We show that even at high temperatures, DM interaction excites QFI of both ferromagnetic and antiferromagnetic models. We also show that QFI of the ferromagnetic model of two qubits can surpass the shot-noise limit of the separable states, while QFI of the antiferromagnetic model in consideration can only approach to the shot-noise limit. Our results open new insights in quantum metrology with Heisenberg models.
Highlights
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology
quantum Fisher information (QFI) of an entangled system of N particles can exceed shot-noise limit (SNL), scaling as N2 in the ideal case, which is the fundamental or so-called Heisenberg limit (HL)[10], achievable by pure GHZ states
We have shown that the Dzyaloshinskii-Moriya interaction excites the quantum Fisher information of the two-qubit and three-qubit Heisenberg models, overwhelming the thermalization effects both in the ferromagnetic and in antiferromagnetic regions
Summary
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. QFI of an entangled system of N particles can exceed SNL (and the system is so called useful for surpassing SNL in quantum metrology), scaling as N2 in the ideal case, which is the fundamental or so-called Heisenberg limit (HL)[10], achievable by pure GHZ states. Decoherence due to inevitable interactions with the environment decreases the QFI of an open system in general This gave rise to devoting an intense effort on QFI with the motivation of finding which systems are useful under which conditions[12,13,14,15,16,17,18,19,20,21,22]. Ma et al showed that as the strength of the decoherence decreases from maximum to a critical point, i) under the amplitude damping, QFI does not increase but rather decreases, and ii) under phase damping, QFI stays constant at 1, the SNL of QFI per particle[17]
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