Beyond Repair: A New Phase of Quantum Information Loss
![The study of the [latex]\mathbb{Z}_N[/latex] toric code under XX-type dephasing reveals a nuanced relationship between code size and quantum information protection, demonstrating that while codes with [latex]N \leq 4[/latex] exhibit a clear transition from fully decodable to completely lost information, larger codes ([latex]N > 4[/latex]) possess an intermediate quasi-long-range order (QLRO) phase where a finite, yet diminishing, fraction of logical information remains protected-a fraction that expands with increasing code size-and critical temperatures consistently approximate 0.38, aligning with self-dual identities.](https://arxiv.org/html/2512.22121v1/x5.png)
New research reveals a distinct phase in decohering quantum codes where information isn’t simply lost, but enters a critical state characterized by limited retrievability.
![The study of the [latex]\mathbb{Z}_N[/latex] toric code under XX-type dephasing reveals a nuanced relationship between code size and quantum information protection, demonstrating that while codes with [latex]N \leq 4[/latex] exhibit a clear transition from fully decodable to completely lost information, larger codes ([latex]N > 4[/latex]) possess an intermediate quasi-long-range order (QLRO) phase where a finite, yet diminishing, fraction of logical information remains protected-a fraction that expands with increasing code size-and critical temperatures consistently approximate 0.38, aligning with self-dual identities.](https://arxiv.org/html/2512.22121v1/x5.png)
New research reveals a distinct phase in decohering quantum codes where information isn’t simply lost, but enters a critical state characterized by limited retrievability.
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