Minimum entangling power is close to its maximum. (English) Zbl 1509.81230
Summary: Given a quantum gate \(U\) acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measures when the inputs are restricted to be product states. In this paper, we mainly focus on the ‘weakest’ one, i.e. the minimum entangling power, among all these entangling powers. We show that, by choosing the entropy of entanglement or Schmidt rank as entanglement measure, even the ‘weakest’ entangling power is generically very close to the maximum possible value of the entanglement measure. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous (for the Hilbert space distance) entanglement measures and generalize our results to multipartite quantum systems.
MSC:
| 81P65 | Quantum gates |
| 81P42 | Entanglement measures, concurrencies, separability criteria |
| 81P55 | Special bases (entangled, mutual unbiased, etc.) |
Keywords:
quantum gate; entangling power; concentration of measure; Riemann geometry; algebraic geometryReferences:
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