Decoherence Enables Information Critical Phases and Fractional Logical Qubit Recovery

The behaviour of information as systems become disordered presents a fundamental challenge in physics, and recent work by Akash Vijay and Jong Yeon Lee, alongside their colleagues, sheds new light on this problem. These researchers define and identify an “information critical phase”, an extended region within disordered systems where information about the original state persists far beyond what conventional theory predicts. They demonstrate the existence of this phase within decohered Toric codes, a type of quantum error-correcting code, revealing that even as the system loses coherence, a finite fraction of logical information remains preserved. This discovery significantly expands our understanding of how memory functions in noisy quantum systems, suggesting the possibility of robust data storage even in the presence of substantial environmental disruption and establishing a new paradigm for fractional topological memory.

Information Critical Phases and Quantum Decoherence

Quantum critical phases are regions of phase space defined by diverging correlation lengths. Researchers now define an information critical phase as an extended region where the information content of a quantum state, measured by the von Neumann entropy, diverges. This work investigates how decoherence, the loss of quantum coherence through environmental interaction, affects entanglement and potentially induces or stabilizes information critical behaviour. The team examines Rényi entropies, measures of entanglement, and demonstrates that under certain conditions, they exhibit scaling behaviour consistent with an information critical phase, even without a conventional quantum critical point. This establishes a connection between decoherence, entanglement, and the emergence of novel quantum phases, offering insights into information’s role in quantum systems and potentially enabling new approaches to quantum control and information processing.

Information Critical Phase in Random Quantum Circuits

Researchers have pioneered a new approach to understanding quantum information preservation in noisy systems by defining and characterizing an “information critical phase. ” They investigated this phase within random quantum circuits, focusing on how entanglement and correlations evolve with increasing noise. A key diagnostic was the development of mutual information between subsystems to pinpoint the emergence of this critical phase, distinct from fully ordered and disordered states. Specifically, the team analyzed the mutual information between two subsystems as a function of a third, demonstrating that in the information critical phase, this mutual information diverges with increasing system size and remains finite even when conditioned on measurements of the third subsystem. Extensive numerical simulations on various quantum circuits and system sizes confirmed these findings, and duality transformations provided deeper insights into the underlying physics. The results suggest that the information critical phase represents a new type of quantum critical point where information is maximally preserved despite noise, opening avenues for designing more resilient quantum technologies.

Information Critical Phase in Decohered Codes

Scientists have identified a novel information critical phase in decohered Toric codes, a breakthrough in understanding quantum error correction and topological memory. The work demonstrates the existence of this phase, characterized by a diverging Markov length, within a specific region of the code’s mixed state phase diagram. This phase appears between reliably decodable and completely failed code states, indicating surprising resilience to noise. The team measured coherent information, assessing the robustness of encoded logical qudits, and found it saturates to a fractional value with increasing system size within the information critical phase.

This saturation signifies that even as the code degrades, a finite fraction of logical information remains preserved. Further analysis reveals the density matrix in this phase decomposes into Coulombic pure states, where anyons reorganize into gapless photons. Investigations into the ungauged Toric code reveal a connection to spontaneous symmetry breaking, where the information critical phase arises from enhanced symmetry, leading to a novel superfluid phase. Crucially, scientists developed an optimal decoding protocol for the noise-corrupted Toric code, achieving a threshold matching the boundary of the decodable phase, and effectively recovering the fractional logical information preserved within the information critical phase, demonstrating a new form of fractional topological memory.

Information Criticality and Fractional Topological Memory

The research team has identified a novel information critical phase within quantum error correction. This phase emerges in systems, such as decohered Toric codes, where the distinctions between reliably encoding quantum information and complete loss of information become blurred. They demonstrate that an extended region exists where the system neither fully protects nor completely destroys logical information, but instead preserves a finite fraction, exhibiting characteristics of a fractional topological memory. This preservation is linked to a unique organization of fundamental particles, transitioning from gapped anyons to gapless photons, and arises from a specific type of symmetry breaking where a weakened symmetry is unexpectedly enhanced.

In a dual model, this enhancement leads to a superfluid phase with coherent excitations involving both the system and its environment. The researchers also developed an optimized decoding protocol capable of recovering the fractional logical information, suggesting practical implications for building more resilient quantum computers. These findings extend the understanding of memory phases by identifying a gapless analog capable of preserving fractional topological memory, opening new avenues for research in quantum information theory and condensed matter physics.