Zhibo Hou

Quantum State Tomography via Linear Regression Estimation

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography.

Full reconstruction of a 14-qubit state within four hours

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without \emph{a priori} knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational complexity of the LRE algorithm is first reduced from

Adaptive quantum state tomography via linear regression estimation: Theory and two-qubit experiment

O(10^{19})

Achieving quantum precision limit in adaptive qubit state tomography

to

Realization of mutually unbiased bases for a qubit with only one wave plate: theory and experiment.

O(10^{15})

Entanglement distribution in optical fibers assisted by nonlocal memory effects

for a 14-qubit state, by dropping all the zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result can play an important role in quantum information technologies with large quantum systems.

Detecting metrologically useful asymmetry and entanglement by a few local measurements

Bo Qi, 2, ∗ Zhibo Hou, 4, ∗ Yuanlong Wang, Daoyi Dong, Han-Sen Zhong, 4 Li Li, Guo-Yong Xiang, 4, † Howard M. Wiseman, Chuan-Feng Li, 4 and Guang-Can Guo 4 Key Laboratory of Systems and Control, ISS, and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, P. R. China Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, People’s Republic of China Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia (Dated: December 8, 2015)

Deterministic realization of collective measurements via photonic quantum walks

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.

Experimentally obtaining maximal coherence via assisted distillation process

We consider the problem of implementing mutually unbiased bases (MUB) for a polarization qubit with only one wave plate, the minimum number of wave plates. We show that one wave plate is sufficient to realize two MUB as long as its phase shift (modulo 360°) ranges between 45° and 315°. It can realize three MUB (a complete set of MUB for a qubit) if the phase shift of the wave plate is within [111.5°, 141.7°] or its symmetric range with respect to 180°. The systematic error of the realized MUB using a third-wave plate (TWP) with 120° phase is calculated to be a half of that using the combination of a quarter-wave plate (QWP) and a half-wave plate (HWP). As experimental applications, TWPs are used in single-qubit and two-qubit quantum state tomography experiments and the results show a systematic error reduction by 50%. This technique not only saves one wave plate but also reduces the systematic error, which can be applied to quantum state tomography and other applications involving MUB. The proposed TWP may become a useful instrument in optical experiments, replacing multiple elements like QWP and HWP.

Experimental test of genuine multipartite nonlocality under the no-signalling principle

The successful implementation of several quantum information and communication protocols requires distributing entangled pairs of quantum bits in a reliable manner. While there exists a substantial amount of recent theoretical and experimental activities dealing with non-Markovian quantum dynamics, experimental application and verification of the usefulness of memory effects for quantum information tasks are still missing. We combine these two aspects and show experimentally that a recently introduced concept of nonlocal memory effects allows to protect and distribute polarization entangled pairs of photons in an efficient manner within polarization-maintaining (PM) optical fibers. The introduced scheme is based on correlating the environments, i.e. frequencies of the polarization entangled photons, before their physical distribution. When comparing to the case without nonlocal memory effects, we demonstrate at least a 12-fold improvement in the channel, or fiber length, for preserving the highly entangled initial polarization states of photons against dephasing.Guo-Yong Xiang‡,1 Zhi-Bo Hou‡,1 Chuan-Feng Li, ∗ Guang-Can Guo, Heinz-Peter Breuer, Elsi-Mari Laine, 4 and Jyrki Piilo † Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China‡ Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany QCD Labs, COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 AALTO, Finland Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland (Dated: January 22, 2014)