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Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain
Quantum Physics · Submitted 4 Jan 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.
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The abstract, sentence by sentence
A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-$\frac{1}{2}$ XX chain. Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-$\frac{1}{2}$ XX chain. | contribution 0.96 | 0.74 | 0.03 | asserted 0.70 |
| s1 | Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. | method 1.00 | 0.95 | 0.02 | asserted 0.97 |
| s2 | Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. | method 1.00 | 0.92 | 0.02 | asserted 1.00 |
| s3 | We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. | result 0.90 | 0.89 | 0.20 | asserted 1.00 |
| s4 | We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing. | interpretation 0.93 | 0.86 | 0.92 | hedged possibility 0.62 |
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Original abstract
A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-$\frac{1}{2}$ XX chain. Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.
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The Jordan-Wigner transformation can be verified using “QuSpin” [ref] a Python package for dynamics and exact diagonalisation of quantum many-body systems.
QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins · The Model · 1.00
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