Abstract
The uncertainty principle, which gives the constraints on obtaining precise outcomes for incompatible measurements, provides a new vision of the real world that we are not able to realize from the classical knowledge. In recent years, numerous theoretical and experimental developments about the new forms of the uncertainty principle have been achieved. Among these efforts, one attractive goal is to find tighter bounds of the uncertainty relation. Here, using an all optical setup, we experimentally investigate a most recently proposed form of uncertainty principle—the fine-grained uncertainty relation assisted by a quantum memory. The experimental results on the case of two-qubit state with maximally mixed marginal demonstrate that the fine-graining method can help to get a tighter bound of the uncertainty relation. Our results might contribute to further understanding and utilizing of the uncertainty principle.
Highlights
Since the original idea of uncertainty principle proposed by Heisenberg in 19271, the uncertainty principle, one of the most remarkable features of quantum mechanics distinguishing from the classical physical world, has been studied for over ninety years with various forms of uncertainty relations achieved, such as standard deviation and entropy[2,3,4]
Soon after the first entropic uncertainty relation for pairs of non-degenerate observables given by Deutsch[14], the popular version of uncertainty relation was conjectured and proved[15,16], which can be extended to a pair of POVM measurements[17]
We report an all-optical experiment to investigate the fine-grained uncertainty relation with the presence of a quantum memory, in the case of a two-qubit state with maximally mixed marginal, one qubit for the system under consideration, the other for the memory
Summary
We report an all-optical experiment to investigate the fine-grained uncertainty relation with the presence of a quantum memory, in the case of a two-qubit state with maximally mixed marginal, one qubit for the system under consideration, the other for the memory. It can be divided into two parts, state preparation and detection. In order to prepare the target state which is determined by the parameters c1 = 0.6, c2 = −0.16, c3 = −0.24, we set the angles of the two HWPs in the loop of TBS, θ1 = θ2 ≈ 26°, which means about 62.1% of the entangled photon 1 ( HH + VV ) is transformed to 1 ( HV + VH ). We need to perform state tomography measurements to evaluate the Berta’s uncertainty bound. These measurement results help to verify the gap between the fine-grained bound and Berta’s bound
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