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arXiv:1203.3356 · International Journal of Theoretical Physics

Conditions for the Freezing Phenomena of Geometric Measure of Quantum Discord for Arbitrary Two-Qubit X-states under Non-dissipative Dephasing Noises

Wei Song, Zhuo‐Liang Cao

Published Sep 25, 2013• 11 citations
arXivHTMLPDF
DOI
10.1007/s10773-013-1835-5

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Physical Review Applied•Nov 25, 2024•0 citations
We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. By relating the expression of the time variation of the discord to the convex function of relative entropy, we obtain the necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditions are applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we show that the same condition and phenomenon coincide in an unusual sort of Bell-diagonal states beyond the standard form.
Several measures of geometric discords have been recently proposed and mostly characterized in qubits. In this work, the dynamics of four measures of geometric discords is studied for two kinds of initial states in the two-qutrit model under environments. It is shown that four indicators can display freezing in Markovian regime and multiple freezing with multiple sudden changes in non-Markovian regime for suitable initial states and model parameters. Moreover, those measures evolve in a similar manner, but they differ from the decaying or increasing rate, the oscillatory amplitude and the time interval of freezing. However, they do not exhibit any freezing for the general Bell states. The dynamical hierarchy is discussed for those indicators. Those are helpful to understand the rich phenomena of discordant dynamics in open qutrits.
Quantum information processing (QIP) based on high-dimensional quantum systems provides unique advantages and new potentials where high-dimensional quantum correlations (QCs) play vital roles. Exploring the resistance of QCs against noises is crucial as QCs are fragile due to complex and unavoidable system-environment interactions. In this study, we investigate the performance of high-dimensional QCs under local dephasing noise using a single nitrogen-vacancy center in diamond. A freezing phenomenon in the high-dimensional quantum discord dynamics was observed, showing that discord is robust against local dephasing noise. Utilizing a robustness metric known as the freezing index, we find that the discord of qutrits outperforms their qubit counterparts when confronted with dephasing noise. Furthermore, we develop a geometric picture to explain this intriguing freezing phenomenon. Our findings highlight the potential of utilizing discord as a physical resource for advancing QIP in high-dimensional quantum settings.