This paper explores a novel type of spontaneous symmetry breaking (SSB) in mixed quantum states, known as strong-to-weak SSB (SW-SSB). SW-SSB occurs when a system with strong symmetry breaks down to weak symmetry. The authors define SW-SSB using the fidelity correlator, which measures the distinguishability between the original state and a state that has broken the strong symmetry. They prove that SW-SSB is a universal property of mixed-state quantum phases, robust against low-depth symmetric local quantum channels. The paper also discusses the stability of SW-SSB under such channels and shows that the broken symmetry cannot be recovered locally. Additionally, the authors argue that thermal states at nonzero temperatures should exhibit SW-SSB, and they study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. Specifically, they show that the SW-SSB transition in a decohered Ising model is equivalent to the decodability transition of the toric code. The paper concludes with a discussion on the recoverability of SW-SSB and the non-invertibility of states with SW-SSB.This paper explores a novel type of spontaneous symmetry breaking (SSB) in mixed quantum states, known as strong-to-weak SSB (SW-SSB). SW-SSB occurs when a system with strong symmetry breaks down to weak symmetry. The authors define SW-SSB using the fidelity correlator, which measures the distinguishability between the original state and a state that has broken the strong symmetry. They prove that SW-SSB is a universal property of mixed-state quantum phases, robust against low-depth symmetric local quantum channels. The paper also discusses the stability of SW-SSB under such channels and shows that the broken symmetry cannot be recovered locally. Additionally, the authors argue that thermal states at nonzero temperatures should exhibit SW-SSB, and they study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. Specifically, they show that the SW-SSB transition in a decohered Ising model is equivalent to the decodability transition of the toric code. The paper concludes with a discussion on the recoverability of SW-SSB and the non-invertibility of states with SW-SSB.