Abstract: The classification of quantum states and operations is an area of common interest between Quantum Information Theory (QIT) and Quantum Many-Body Physics (QMBP). However, while in QIT one is typically interested in classifying states up to transformations that do not increase entanglement (LOCC), phases of matter in QMBP are defined in terms of unitary transformations that preserve locality, i.e. shallow quantum circuits. In this talk, motivated by the advent of noisy intermediate-scale quantum devices, I will introduce deterministic state-transformation protocols between many-body quantum states that can be implemented by low-depth quantum circuits followed by LOCC. I will show that this gives rise to a different classification of phases in which topologically ordered states or other paradigmatic entangled states become trivial. In this setting, I will provide a full classification of phases in 1D in the context of matrix product states. Finally, I will discuss how the set of unitary operations is enhanced by LOCC, allowing one to perform certain large-depth quantum circuits in terms of low-depth ones.
Based on: LP, G. Styliaris, J. I. Cirac, Phys. Rev. Lett. 127, 220503 (2021); arXiv: 2103.13367
