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Register a new userExperimental Adaptive Quantum Tomography of Two-Qubit States
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We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Huszar and N.M.T.Houlsby, Phys.Rev.A 85, 052120 (2012)] and provides an optimal measurement approach in terms of the information gain. We address the practical questions, which one faces in any experimental application: the influence of technical noise, and behavior of the tomographic algorithm for an easy to implement class of factorized measurements. In an experiment with polarization states of entangled photon pairs we observe a lower instrumental noise floor and superior reconstruction accuracy for nearly-pure states of the adaptive protocol compared to a non-adaptive. At the same time we show, that for the mixed states the restriction to factorized measurements results in no advantage for adaptive measurements, so general measurements have to be used.
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Tomography of the two qubit density matrix shared by Alice and Bob is an essential ingredient for guaranteeing an acceptable margin of confidentiality during the establishment of a secure fresh key through the Quantum Key Distribution (QKD) scheme. We show how the Singapore protocol for key distribution is optimal from this point of view, due to the fact that it is based on so called SIC POVM qubit tomography which allows the most accurate full tomographic reconstruction of an unknown density matrix on the basis of a restricted set of experimental data. We illustrate with the help of experimental data the deep connections that exist between SIC POVM tomography and discrete Wigner representations. We also emphasise the special role played by Bell states in this approach and propose a new protocol for Quantum Key Distribution during which a third party is able to concede or to deny A POSTERIORI to the authorized users the ability to build a fresh cryptographic key.
Adaptive techniques have important potential for wide applications in enhancing precision of quantum parameter estimation. We present a recursively adaptive quantum state tomography (RAQST) protocol for finite dimensional quantum systems and experimentally implement the adaptive tomography protocol on two-qubit systems. In this RAQST protocol, an adaptive measurement strategy and a recursive linear regression estimation algorithm are performed. Numerical results show that our RAQST protocol can outperform the tomography protocols using mutually unbiased bases (MUB) and the two-stage MUB adaptive strategy even with the simplest product measurements. When nonlocal measurements are available, our RAQST can beat the Gill-Massar bound for a wide range of quantum states with a modest number of copies. We use only the simplest product measurements to implement two-qubit tomography experiments. In the experiments, we use error-compensation techniques to tackle systematic error due to misalignments and imperfection of wave plates, and achieve about 100-fold reduction of the systematic error. The experimental results demonstrate that the improvement of RAQST over nonadaptive tomography is significant for states with a high level of purity. Our results also show that this recursively adaptive tomography method is particularly effective for the reconstruction of maximally entangled states, which are important resources in quantum information.
Full quantum state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr3+ ions, doped into a Y2SiO5 crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Moelmer dark state scheme. Fidelities above >90%, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Moelmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.
We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for adaptive strategies. For pure states we observe close to 1/N scaling of infidelity with overall number of registered events, while best non-adaptive protocols allow for $1/sqrt{N}$ scaling only. Experiments are performed for polarization qubits, but the approach is readily adapted to any dimension.
The precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to the subtle information tradeoff among incompatible observables. In the case of a qubit, the theoretic precision limit was determined by Hayashi as well as Gill and Massar, but attaining the precision limit in experiments has remained a challenging task. Here we report the first experiment which achieves this precision limit in adaptive quantum state tomography on optical polarization qubits. The two-step adaptive strategy employed in our experiment is very easy to implement in practice. Yet it is surprisingly powerful in optimizing most figures of merit of practical interest. Our study may have significant implications for multiparameter quantum estimation problems, such as quantum metrology. Meanwhile, it may promote our understanding about the complementarity principle and uncertainty relations from the information theoretic perspective.
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