Separability transitions in topological states induced by local decoherence
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910425669435392 |
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| author | Chen, Yu-Hsueh Grover, Tarun |
| author_facet | Chen, Yu-Hsueh Grover, Tarun |
| contents | We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled (SRE) pure states. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions that precisely coincide with the threshold for the feasibility of active error correction. A key insight is that local decoherence acting on the 'parent' cluster states of these models results in a Gibbs state. As an example, for the 2d (3d) toric code subjected to bit-flip errors, we show that the decohered density matrix can be written as a convex sum of SRE states for $p > p_c$, where $p_c$ is related to the paramagnetic-ferromagnetic transition in the 2d (3d) random-field bond Ising model along the Nishimori line. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_11879 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separability transitions in topological states induced by local decoherence Chen, Yu-Hsueh Grover, Tarun Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We study states with intrinsic topological order subjected to local decoherence from the perspective of separability, i.e., whether a decohered mixed state can be expressed as an ensemble of short-range entangled (SRE) pure states. We focus on toric codes and the X-cube fracton state and provide evidence for the existence of decoherence-induced separability transitions that precisely coincide with the threshold for the feasibility of active error correction. A key insight is that local decoherence acting on the 'parent' cluster states of these models results in a Gibbs state. As an example, for the 2d (3d) toric code subjected to bit-flip errors, we show that the decohered density matrix can be written as a convex sum of SRE states for $p > p_c$, where $p_c$ is related to the paramagnetic-ferromagnetic transition in the 2d (3d) random-field bond Ising model along the Nishimori line. |
| title | Separability transitions in topological states induced by local decoherence |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.11879 |