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Register a new userExperimental test of error-tradeoff uncertainty relation using a continuous-variable entangled state
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Heisenbergs original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenbergs error-disturbance uncertainty relation can be violated in some cases. We experimentally test the error-tradeoff 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 error-tradeoff 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 Heisenbergs error-tradeoff uncertainty relation is violated in some cases for a continuous-variable system, while the Ozawas and Brainciards relations are valid.
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Uncertainty relation is one of the fundamental principle in quantum mechanics and plays an important role in quantum information science. We experimentally test the error-disturbance uncertainty relation (EDR) with continuous variables for Gaussian states. Two conjugate continuous-variable observables, amplitude and phase quadratures of an optical mode, are measured simultaneously by using a heterodyne measurement system. The EDR with continuous variables for a coherent state, a squeezed state and a thermal state are verified experimentally. Our experimental results demonstrate that Heisenbergs EDR with continuous variables is violated, yet Ozawas and Branciards EDR with continuous variables are validated.
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the uncertainty relations which mainly focus on the pure states. Here we present an experimental investigation on the optimal majorization uncertainty for mixed states by means of the coherent light. The polarization states with adjustable mixedness are prepared by the combination of two coherent beams, and we test the majorization uncertainty relation for three incompatible observables using the prepared mixed states. The experimental results show that the direct sum majorization uncertainty relations are tight and optimal for general mixed systems.
A continuous-variable tripartite entangled state is experimentally generated by combining three independent squeezed vacuum states and the variances of its relative positions and total momentum are measured. We show that the measured values violate the separability criteria based on the sum of these quantities and prove the full inseparability of the generated state.
We propose and demonstrate experimentally a scheme to create entangled history states of the Greenberger-Horne-Zeilinger (GHZ) type. In our experiment, the polarization states of a single photon at three different times are prepared as a GHZ entangled history state. We define a GHZ functional which attains a maximum value $1$ on the ideal GHZ entangled history state and is bounded above by $1/16$ for any three-time history state lacking tripartite entanglement. We have measured the GHZ functional on a state we have prepared experimentally, yielding a value of $0.656pm 0.005$, clearly demonstrating the contribution of entangled histories.
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenbergs original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [Phys. Rev. Lett. 111, 160405 (2013); Phys. Rev. A 89, 012129 (2014)]. Here we reform their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible but typically non-commutative observables on one qubit are measured simultaneously.
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