Quantum Metrology: Surpassing the shot-noise limit with Dzyaloshinskii-Moriya interaction

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.

Parameter estimation with Dzyaloshinskii–Moriya interaction under external magnetic fields

“…An interesting point here is that although resulting in different systems, therefore different corresponding density matrices and different entanglement values, inhomogeneous magnetic field and DM interaction excite the QFI in the same way. Exhibiting first a sudden increase and then a slow decrease with respect to increasing B, b or D, the QFI of ferromagnetic chain remains well larger than that of antiferromagnetic chain, surpassing the shotnoise level, in accordance with our recent findings for the XXX model including only DM interaction [35]. By fixing the temperature at T = 0.7, we explore the effects of DM interaction and magnetic fields together, and homogeneous and inhomogeneous magnetic fields together in QFI in Fig.2.…”

Dzyaloshinskii-Moriya interaction as a fast quantum information scrambler

“…Sharma et al studied entanglement sudden death and birth [7] and entanglement dynamics [8] of qubit-qutrit systems, also of Werner states [9] and qubit-qutrit systems with x-component DM interaction [10]. Because, unlike entanglement mea-sures, quantum Fisher information (QFI) is not an entanglement monotone that it can be increased via local operations and classical communications [11], we asked whether it can be excited via DM interaction too, and showed that it can be [12,13]. Bound entanglement (BE) [14] and its activation are among the most interesting phenomena in quantum mechanics [15,16].…”

Positive impact of decoherence on spin squeezing in GHZ and W states

“…Enhancement of sensitivity and precision in quantum metorology [14,15] is an important aspect which has been achieved by using many techniques, spin squeezing is one of these. Squeezing of spins play an important role for quantum metrology and magnetometery to improve the sensitivity and precision because of its ability to reduce the quantum noise [16][17][18][19][20]. Early experimental manifestations of spin squeezing is demonstrated in varieties of physical systems such as, in entangled ion trap systems [21], in Bose-Einstein condensate (BEC) through repulsive interactions [22], measurements by partial projection [23], squeezing of huge ensemble of atoms in cavities through light-matter interaction to produce atomic clocks [24][25][26][27][28][29][30], gravitational interferometers [31][32][33] and in many qubit systems [34][35][36].…”