This paper explores a novel type of spontaneous symmetry breaking (SSB) in mixed quantum states, called strong-to-weak SSB (SW-SSB). In mixed states, symmetry can manifest in two forms: strong symmetry, where each individual pure state in the ensemble has the same symmetry charge, and weak symmetry, which applies to the entire ensemble. SW-SSB occurs when a strong symmetry is broken to a weak one. The paper defines SW-SSB using the fidelity correlator, which measures the long-range order of a local operator in a mixed state. It proves that SW-SSB is a universal property of mixed-state quantum phases, robust against symmetric low-depth local quantum channels. The paper also shows that symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. It argues that a thermal state at a nonzero temperature in the canonical ensemble should have spontaneously broken strong symmetry. The paper studies non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. It also discusses the recoverability of the decohered Ising model and the equivalence of different definitions of SW-SSB. The paper concludes that SW-SSB is a fundamental property of mixed-state quantum phases and has important implications for symmetry-protected topological phases.This paper explores a novel type of spontaneous symmetry breaking (SSB) in mixed quantum states, called strong-to-weak SSB (SW-SSB). In mixed states, symmetry can manifest in two forms: strong symmetry, where each individual pure state in the ensemble has the same symmetry charge, and weak symmetry, which applies to the entire ensemble. SW-SSB occurs when a strong symmetry is broken to a weak one. The paper defines SW-SSB using the fidelity correlator, which measures the long-range order of a local operator in a mixed state. It proves that SW-SSB is a universal property of mixed-state quantum phases, robust against symmetric low-depth local quantum channels. The paper also shows that symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. It argues that a thermal state at a nonzero temperature in the canonical ensemble should have spontaneously broken strong symmetry. The paper studies non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. It also discusses the recoverability of the decohered Ising model and the equivalence of different definitions of SW-SSB. The paper concludes that SW-SSB is a fundamental property of mixed-state quantum phases and has important implications for symmetry-protected topological phases.