Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions

• URL: http://arxiv.org/abs/2002.01590v1
• Date: Wed, 5 Feb 2020 00:45:21 GMT
• Title: Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions
• Authors: Andr\'e T. Ces\'ario and Diego L. B. Ferreira and Tiago Debarba and Fernando Iemini and Thiago O. Maciel and Reinaldo O. Vianna
• Abstract summary: We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
• Score: 55.41644538483948
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in the correlation distributions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.

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