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

2021 ◽  
Author(s):  
Asad Ali ◽  
Mustansar N Nadeem ◽  
A.H Toor ◽  
Junaid Ulhaq ◽  
Shah Ahad
Keyword(s):  
Quantum Coherence ◽  
Coupling Parameter ◽  
Quantum Fisher Information ◽  
Quantitative Relationship ◽  
Bath Temperature ◽  
Reciprocal Relationship ◽  
Entanglement Measure ◽  
Thermal Entanglement ◽  
Xxx Model ◽  
Heisenberg Xxx Model

We study the validity of quantum Fisher information (QFI) as a faithful quantum coherence and correlation quantier by drawing a comparison with subsystem's coherence measure, rst-order coherence (FOC) and the entanglement measure, Negativity to study the behavior of thermal quantum coherence and correlations in two qubit Heisenberg XXX model, placed in independently controllable magnetic eld by systematically varying the coupling parameter, magnetic eld and bath temperature for ferromagnetic and antiferromagnetic case. After carefully observing the prole of quantum coherence and correlation measures, we propose an inequality relations which shows that there may exist a quantitative relationship between QFI, Negativity and FOC in which, the equality exists at zero temperature. We identify QFI to be a more useful coherence quantier, as it quanties coherence of individual subsystems and correlations among the subsystems. On the other hand, FOC identies coherence present in the individual subsystems only. A reciprocal relationship between Negativity and FOC is also observed in dierent cases. We also observe the existence of entanglement in ferromagnetic case, in contrast to simple Heisenberg XXX model in uniform magnetic eld. We show that in the ferromagnetic case, a very small inhomogeneity in magnetic eld is capable of producing large values of thermal entanglement. This shows that the behavior of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic elds, which is inevitably present in any solid state realization of qubits.

scholarly journals Thermal Quantum Coherence properties in Two-Qubit Heisenberg XXX Model in Nonhomogeneous Magnetic Field

2021 ◽  
Author(s):  
Asad Ali ◽  
Muhammad Anees Khan
Keyword(s):  
Magnetic Field ◽  
Quantum Coherence ◽  
Uniform Magnetic Field ◽  
Coupling Parameter ◽  
Magnetic Interaction ◽  
Threshold Value ◽  
Quantum Correlations ◽  
Qubit System ◽  
Xxx Model ◽  
Heisenberg Xxx Model

We investigate the behavior of thermal quantum coherence in the Heisenberg XXX model for a two-qubit system placed in independently controllable Inhomogeneous magnetic fields applied to two qubits respectively. We discuss the behavior of quantum coherence by systematically varying the coupling parameter, magnetic field, and temperature for both ferromagnetic and antiferromagnetic cases. The results show the interesting behavior of quantum coherence in a certain range of parameters. Generally, it is observed that quantum correlations decay with temperature, but in the ferromagnetic case with uniform magnetic interaction, it rises with temperature up to a certain threshold value and ultimately it decreases its value to zero. Moreover, it is observed that preserving the quantum coherence for small temperatures is very hard with the increasing magnetic field because, at small temperatures, quantum coherence decays sharply with the increase in magnetic field whereas at larger temperatures it decays completely at fairly large values of the magnetic field. The variation of quantum coherence with uniform magnetic field in the antiferromagnetic case is observed to be Gaussian for larger temperature but at zero or nearly zero temperature, it behaves as a constant function for uniform magnetic field up to a threshold value and then decays to zero with an infinite slope. This shows the signature of quantum phase transition from quantum nature to classicality.

Thermal entanglement in a mixed spin Heisenberg XXX chain with DM interaction

2021 ◽  
pp. 2150021
Author(s):  
Nizar Ahami ◽  
Morad El Baz
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Thermal Entanglement ◽  
Bipartite Entanglement ◽  
Dm Interaction ◽  
One Dimensional ◽  
Mixed Spin ◽  
Xxx Model ◽  
Moriya Interaction ◽  
Heisenberg Xxx Model

We consider a one-dimensional, mixed spin Heisenberg XXX model with an homogeneous external magnetic field and Dzyaloshinskii–Moriya interaction. Alternating spin-[Formula: see text] and spin-1 particles are forming the chain. The effect of the different parameters of the system on the bipartite thermal entanglement is studied. The type of chain used (mixed) and the size of the chain ([Formula: see text]) allow to study three types of bipartite entanglement, the qubit–qubit, qubit–qutrit and qutrit–qutrit thermal entanglement.

Detecting Violation of Bell Inequalities using LOCC Maximized Quantum Fisher Information and Entanglement Measures

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Fisher Information ◽  
Quantum Fisher Information ◽  
Bell Inequalities ◽  
Light Signal ◽  
Entanglement Measure ◽  
Bell’S Inequalities ◽  
Entanglement Measures ◽  
Bell's Inequalities ◽  
System States ◽  
Random Quantum States

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

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