Researchers Unlock Symmetry-protected Topological Phases in Open Quantum Systems, Offering Robust States

Researchers propose a tensor network approach, known as the locally purified density operator (LPDO), to investigate the classification and characterization of symmetry-protected topological phases in open quantum systems. The team extends the concept of injectivity, originally associated with matrix product states and projected entangled pair states, to LPDOs in both one and two dimensions, revealing two distinct types of injectivity conditions inherent in short-range entangled density matrices, providing a new tool for understanding topological order in open quantum systems.

Mixed States and Symmetry-Protected Topology

This work focuses on the theoretical classification of quantum phases of matter, particularly within the context of mixed states, statistical mixtures of states, and symmetry-protected topological phases (SPTs). The research addresses a crucial challenge: understanding these phases in realistic systems subject to environmental noise and decoherence, as real-world quantum systems almost always exist in mixed states due to interactions with their surroundings. The team utilizes locally purified density operators (LPDOs) as a key technique to simplify the analysis of mixed states and reveal hidden topological order, investigating average symmetries and anomalies which can indicate non-trivial topological order. Tensor networks, such as matrix product states and operators, serve as a major computational tool for representing and manipulating quantum states, especially in lower-dimensional systems. The overarching goal is to develop a robust framework for classifying different quantum phases of matter, even when the system is in a mixed state and subject to decoherence, employing techniques like purification, renormalization groups, and quantum simulation. This work pushes the boundaries of our understanding of quantum phases by focusing on realistic mixed-state systems, developing new theoretical tools, utilizing powerful computational techniques, and exploring the role of symmetry and anomalies in stabilizing topological order.

Average Symmetry-Protected Phases in Noisy Systems

Researchers have established a new framework for understanding symmetry-protected topological phases, extending the concept to open, noisy quantum systems. These systems interact with their environment, revealing previously hidden quantum states. The team discovered that these phases, termed average symmetry-protected topological (ASPT) phases, arise from a unique interplay between strong and weak symmetries within mixed quantum states, unlike traditional topological phases found in isolated systems. This work demonstrates that ASPT phases can exist even when no corresponding phase exists in pure, undisturbed quantum systems, expanding the known landscape of quantum matter.

The breakthrough centers on a novel application of locally purified density operators (LPDOs), a mathematical tool for representing the complex states of open quantum systems. By extending concepts from matrix product states to LPDOs in both one and two dimensions, scientists unveiled two distinct types of injectivity conditions crucial for characterizing short-range entangled density matrices, providing an intuitive and explicit construction of ASPT states and a “decorated domain-wall picture” that clarifies their underlying structure. Experiments revealed that these ASPT phases are protected by both a weak global symmetry and a strong fermion parity symmetry, and the framework extends to accommodate general group structures. Researchers derived both the classification data and the explicit forms of obstruction functions using the LPDO formalism, particularly in cases where symmetries interact in complex ways, constructing fixed-point LPDOs for ASPT phases in both one and two dimensions, demonstrating their potential physical realization in systems subject to decoherence or disorder, and opening new avenues for designing robust quantum states and potentially leading to advancements in resilient quantum information processing and error correction strategies.

Fermion Parity Defines Topological Phase Stability

This research introduces a new framework for understanding symmetry-protected topological phases in quantum systems, specifically those operating in open and noisy environments. The team demonstrates that these phases, which rely on specific symmetries to remain stable, can be accurately described using a novel approach based on locally purified density operators (LPDOs) and tensor networks, revealing how topological invariants arise from the interplay between strong and weak symmetries within the system. The key finding is that the topological classification of these phases depends on the fermion parity and the weak symmetry group present in the system, identifying specific conditions that these properties must satisfy to guarantee the existence of a stable topological phase. Importantly, the framework accurately captures the characteristics of these phases, including their decorated domain-wall structure, in a concise and interpretable manner. The authors acknowledge that their framework focuses on systems with a strong fermion parity symmetry and a weak symmetry group, and further investigation is needed to explore other symmetry configurations. Future research directions include extending this approach to more complex systems and exploring the implications for designing robust quantum devices, hoping this work will contribute to the development of more stable and reliable quantum technologies by providing a deeper understanding of how to protect quantum states from environmental noise.