Geometric methods and applications: for computer science and engineering
Geometric methods and applications: for computer science and engineering
Quantum computation and quantum information
Quantum computation and quantum information
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Entanglement of formation and concurrence
Quantum Information & Computation
Strong NP-hardness of the quantum separability problem
Quantum Information & Computation
Quantum Information & Computation
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Given a bipartite quantum state ρ with subsystems A and B of arbitrary dimensions, we study the entanglement detecting capabilities of locally noneffective, or cyclic, unitary operations [L. B. Fu, Europhys. Lett., vol. 75, pp. 1-7, 2006]. Local cyclic unitaries have the special property that they leave their target subsystem invariant. We investigate the distance between ρ and the global state after local application of such unitaries as a possible indicator of entanglement. To this end, we derive and discuss closed formulae for the maximal such distance achievable for three cases of interest: (pseudo)pure quantum states, Werner states, and two-qubit states. What makes this criterion interesting, as we show here, is that it surprisingly displays behavior similar to recent anomalies observed for non-locality measures in higher dimensions, as well as demonstrates an equivalence to the CHSH inequality for certain classes of two-qubit states. Yet, despite these similarities, the criterion is not itself a non-locality measure. We also consider entanglement detection in bound entangled states.