Channeling Quantum Criticality

We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a g function in conformal field theory, allowing us to define a notion of renormalization group (RG) flow (or phase transitions) between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the conformal field theory. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.

Automated summary

We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and find universal properties of entanglement in resulting mixed states. We define a renormalization group flow between quantum channels and relate the subleading logarithmic scaling of subsystem entropy to correlation functions in conformal field theory. We also show that the subsystem entanglement negativity can exhibit different scaling behaviors based on the renormalization group flow. Our results are important for understanding quantum critical states in noisy quantum simulators.