Spontaneous Symmetry Breaking in Mixed Quantum States: From Strong to Weak

核心概念

This paper introduces the concept of strong-to-weak spontaneous symmetry breaking (SW-SSB) in mixed quantum states, explores its properties, and demonstrates its presence in various physical systems, including thermal states and decohered quantum models.

摘要

Lessa, L. A., Ma, R., Zhang, J.-H., Bi, Z., Cheng, M., & Wang, C. (2024). Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States. arXiv:2405.03639v3 [quant-ph].

This paper aims to define and explore a novel type of spontaneous symmetry breaking (SSB) in mixed quantum states, termed strong-to-weak SSB (SW-SSB), where a strong symmetry (present in each pure state of the ensemble) is broken to a weak one (present only in the entire ensemble).

從以下內容提煉的關鍵洞見

Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States

by Leonardo A. ... 於 arxiv.org 11-19-2024

https://arxiv.org/pdf/2405.03639.pdf

深入探究

How can the concept of SW-SSB be applied to understand the behavior of open quantum systems in realistic experimental settings?

The concept of SW-SSB provides a valuable framework for understanding the behavior of open quantum systems in realistic experimental settings, where noise and decoherence are unavoidable. Here's how:

Characterizing Robust Quantum Phases: SW-SSB, particularly when defined through the fidelity correlator, exhibits robustness against certain types of noise. This robustness makes it a useful tool for characterizing stable quantum phases in open systems. Experimentalists can use techniques like classical shadow tomography to measure the fidelity correlator (or the more accessible R´enyi-2 correlator as a proxy) and identify phases exhibiting SW-SSB. These phases, by their nature, would possess a degree of inherent resilience against noise, making them potentially relevant for quantum information processing tasks.

Understanding Decoherence Mechanisms: SW-SSB can shed light on the mechanisms of decoherence in open systems. By studying how different types of noise affect the fidelity correlator, researchers can gain insights into how quantum correlations are lost due to interactions with the environment. For instance, the examples of the decohered Ising model and the quantum rotor model illustrate how decoherence can drive transitions into SW-SSB phases.

Engineering Noise-Resilient States: Understanding SW-SSB can guide the development of strategies for engineering noise-resilient quantum states. By identifying the conditions under which strong symmetries are preserved as weak symmetries, researchers can potentially design systems and protocols that are less susceptible to specific decoherence channels. This knowledge could be particularly relevant for developing more robust quantum memories or communication channels.

Experimental Signatures: The local indistinguishability and detectability properties of SW-SSB states offer potential experimental signatures. While distinguishing states with different strong symmetry charges might require global measurements, the local indistinguishability suggests that local measurements would be insufficient. This distinction provides an experimentally verifiable characteristic of SW-SSB.

Could there be cases where a mixed state exhibits SW-SSB without any underlying strong symmetry in the first place?

The concept of SW-SSB, as defined in the provided text, inherently relies on the presence of an underlying strong symmetry that gets broken down to a weak symmetry. Therefore, a mixed state cannot exhibit SW-SSB without an initial strong symmetry.
Here's why:

Definition: SW-SSB specifically describes a scenario where a strong symmetry, present in each pure state within a mixed state ensemble, is broken at the ensemble level, leaving only a weak symmetry.

Charged Operators: The definitions of both the fidelity correlator and the R´enyi-2 correlator, used to diagnose SW-SSB, rely on the existence of charged local operators. These operators transform non-trivially under the strong symmetry. Without a strong symmetry, the notion of a "charged" operator becomes ill-defined.

Physical Interpretation: The physical interpretation of SW-SSB revolves around the idea that the system, while not exchanging charges with the environment (hence possessing strong symmetry), explores different symmetry sectors within the ensemble. This exploration leads to the breaking of the strong symmetry at the ensemble level. Without an initial strong symmetry, this physical picture breaks down.

What are the implications of SW-SSB for the development of fault-tolerant quantum computers, considering that noise and decoherence are inevitable in real-world systems?

The phenomenon of SW-SSB has significant implications, both positive and potentially challenging, for the development of fault-tolerant quantum computers:
Potential Advantages:

Identifying Robust Subspaces: The robustness of SW-SSB against certain noise models, as highlighted by the stability theorems, suggests the existence of decoherence-protected subspaces within the Hilbert space. These subspaces could be potentially exploited to encode and manipulate quantum information in a noise-resilient manner.

New Error-Correction Strategies: Understanding SW-SSB might inspire novel error-correction strategies. Traditional quantum error correction often focuses on preserving global symmetries. However, the concept of SW-SSB suggests that even in the presence of noise that breaks strong symmetries, weaker symmetries might persist and be leveraged for error correction.

Characterizing Noise: Studying SW-SSB in open quantum systems can provide valuable information about the nature of the noise affecting the system. By analyzing how different noise models lead to SW-SSB, researchers can gain insights into the dominant decoherence channels and develop targeted strategies for noise mitigation.
Potential Challenges:

Limited Computational Power: While SW-SSB phases exhibit stability against certain types of noise, they might not possess the same computational power as pure-state symmetry-broken phases. The inherent mixedness of these states could limit the range of quantum operations that can be reliably performed.

Complexity of Characterization: Determining whether a particular state exhibits SW-SSB, especially using the fidelity correlator, can be experimentally challenging. Efficient methods for characterizing SW-SSB in large systems are crucial for harnessing its potential in fault-tolerant quantum computation.

New Error Channels: The very nature of SW-SSB, where strong symmetries are broken, implies that conventional error correction techniques relying on these symmetries might not be directly applicable. New error channels, specific to the broken strong symmetries, would need to be considered and addressed.
In summary, SW-SSB presents both opportunities and challenges for fault-tolerant quantum computation. By understanding the properties of SW-SSB phases and developing techniques to control and manipulate them, researchers can potentially harness their noise resilience while mitigating their limitations.