An algorithm to explore entanglement in small systems

Abstract

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels.

Published version, 20 pages

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• Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
• Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States
• Finding maximal quantum resources
• Derivation of the robustness from the concurrence
• Lower bound on entanglement in subspaces defined by Young diagrams
• Symmetric tensor scars with tunable entanglement from volume to area law