Persistent Topological Negativity in a High-Temperature Mixed-State

• URL: http://arxiv.org/abs/2408.00066v1
• Date: Wed, 31 Jul 2024 18:00:00 GMT
• Title: Persistent Topological Negativity in a High-Temperature Mixed-State
• Authors: Yonna Kim, Ali Lavasani, Sagar Vijay,
• Abstract summary: We study the entanglement structure of the Greenberger-Horne-Zeilinger (GHZ) state as it thermalizes under a strongly-symmetric quantum channel. We show that the topological entanglement negativity of a large region is insensitive to this transition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the entanglement structure of the Greenberger-Horne-Zeilinger (GHZ) state as it thermalizes under a strongly-symmetric quantum channel describing the Metropolis-Hastings dynamics for the $d$-dimensional classical Ising model at inverse temperature $\beta$. This channel outputs the classical Gibbs state when acting on a product state in the computational basis. When applying this channel to a GHZ state in spatial dimension $d>1$, the resulting mixed state changes character at the Ising phase transition temperature from being long-range entangled to short-range-entangled as temperature increases. Nevertheless, we show that the topological entanglement negativity of a large region is insensitive to this transition and takes the same value as that of the pure GHZ state at any finite temperature $\beta>0$. We establish this result by devising a local operations and classical communication (LOCC) ``decoder" that provides matching lower and upper bounds on the negativity in the thermodynamic limit which may be of independent interest. This perspective connects the negativity to an error-correction problem on the $(d-1)$-dimensional bipartitioning surface and explains the persistent negativity in certain correlated noise models found in previous studies. Numerical results confirm our analysis.

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