[This paper is part of the Focused Collection on Upper Division Physics Courses.] Standardized assessment tests that allow researchers to compare the performance of students under various curricula are highly desirable. There are several research-based conceptual tests that serve as instruments to assess and identify students' difficulties in lower-division courses....
We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space
corresponding to 2N qubits (N qubits in each subsystem). Our construction provides a method of generalization
of the Robertson map that naturally meshes with 2N-qubit systems, i.e., its structure respects the 2[superscript 2N]...
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call Local Topological Quantum Order and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result...