Information exchange symmetry breaking in quantum-enhanced experiments

A quantum-enhanced experiment, in which quantum information is transduced from a system of interest and processed on a quantum computer, has the possibility of exponential advantage in sampling tasks over a traditional experiment, in which only the measurement outcomes of projective or weak measurements are stored on a classical computer. In this work, we demonstrate that, similar to the measurement induced phase transition~(MIPT) occurring in traditional experiments, quantum-enhanced experiments can also show entanglement phase transitions. We identify an information exchange symmetry which is spontaneously broken both in the MIPT and in a class of quantum-enhanced experiments obeying this symmetry. The symmetry requires that the information recorded in the classical or quantum computer is as informative about the dynamics of the system as the information lost into the environment. We introduce a noisy transduction operation, and show that it satisfies this symmetry. The noisy transduction operation acts independently on two qubits, recording the quantum state of one qubit in the measurement apparatus, while erasing the quantum state of the other qubit with the environment. We then construct a random brickwork circuit which shows an entanglement transition tuned by the rate of noisy transduction operations. The symmetric phase of such transition is characterized by area law entanglement, where the subsystem entropy conditioned on the quantum states in the apparatus does not scale with system size, while the symmetry broken phase is characterized by volume law scaling entanglement. Our work introduces a quantum generalization of the MIPT entanglement transitions, and provides a unified framework to understand both as a spontaneous symmetry breaking of the information exchange symmetry.