Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements

Symmetry breaking plays a central role in classifying the phases of quantum many-body systems. Recent developments have highlighted a novel symmetry-breaking pattern, in which the strong symmetry of a density matrix spontaneously breaks to the week symmetry. This strong-to-weak symmetry breaking is typically detected using multi-replica correlation functions, such as the R\'enyi-2 correlator. In this letter, we propose a practical protocol for detecting strong-to-weak symmetry breaking in experiments using the randomized measurement toolbox. Our scheme involves collecting the results of random Pauli measurements for (i) the original quantum state and (ii) the quantum state after evolution with the charged operators. Based on the measurement results, with a large number of samples, we can obtain the exact solution to the R\'enyi-2 correlator. With a small sample size, we can still provide an alternative approach to estimate the phase boundary to a decent accuracy. We perform numerical simulations of Ising chains with all-to-all decoherence as an exemplary demonstration. Our result opens the opportunity for the experimental studies of the novel quantum phases in mixed quantum states.