Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. The Fisher information is widely used in quantum metrology since it is related to the quantum gain in metrology measurements. Here we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an upper separability bound for each partition. An entanglement witness is constructed by comparing the two quantities. Our analysis demonstrates the usefulness of these methods for continuous-variable systems and provides a detailed geometric understanding of the robustness of cluster-state entanglement under photon losses. arXiv:1804.08296v2 [quant-ph]
Einstein–Podolsky–Rosen (EPR) steering is one of the most intriguing features of quantum mechanics and an important resource for quantum communication. For practical applications, it remains a challenge to protect EPR steering from decoherence due to its intrinsic difference from entanglement. Here, we experimentally demonstrate the distillation of Gaussian EPR steering and entanglement in lossy and noisy environments using measurement-based noiseless linear amplification. Different from entanglement distillation, the extension of steerable region happens in the distillation of EPR steering, besides the enhancement of steerabilities. We demonstrate that the two-way or one-way steerable region is extended after the distillation of EPR steering when the NLA is implemented based on Bob’s or Alice’s measurement results. We also show that the NLA helps to extract the secret key from the insecure region in one-sided device-independent quantum key distribution with EPR steering. Our work paves the way for quantum communication exploiting EPR steering in practical quantum channels.
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's errordisturbance uncertainty relation can be violated in some cases. We experimentally test the errortradeoff uncertainty relation by using a continuous-variable Einstein-Podolsky-Rosen (EPR) entangled state. Based on the quantum correlation between the two entangled optical beams, the errors on amplitude and phase quadratures of one EPR optical beam coming from joint measurement are estimated respectively, which are used to verify the error-tradeoff relation. Especially, the errortradeoff relation for error-free measurement of one observable is verified in our experiment. We also verify the error-tradeoff relations for nonzero errors and mixed state by introducing loss on one EPR beam. Our experimental results demonstrate that Heisenberg's error-tradeoff uncertainty relation is violated in some cases for a continuous-variable system, while the Ozawa's and Brainciard's relations are valid.I.
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