Multipartite entanglement of the topologically ordered state in a perturbed toric code

We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$frac{1}{2}$ toric code model on a square lattice with external fields. We show that the QFI density of the ground state can be written in terms of the expectation values of gauge-invariant Wilson loops for different sizes of square regions and identify $mathbb{Z}_2$ topological order by its scaling behavior. Furthermore, we use this multipartite entanglement witness to investigate thermalization and disorder-assisted stabilization of topological order after a quantum quench. Moreover, with an upper bound of the QFI, we demonstrate the absence of finite-temperature topological order in the 2D toric code model in the thermodynamic limit. Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.

Metrological characterisation of non-Gaussian entangled states of superconducting qubits

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalisation of the RSP with respect to nonlinear observables, and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, here we report the characterisation of multiparticle entangled states generated during its nonlinear dynamics. First, selecting 10 qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89$^{+0.28}_{-0.29}$ dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Protecting topological order by dynamical localization

As a prototype model of topological quantum memory, two-dimensional toric code is genuinely immune to generic local static perturbations, but fragile at finite temperature and also after non-equilibrium time evolution at zero temperature. We show that dynamical localization induced by disorder makes the time evolution a local unitary transformation at all times, which keeps topological order robust after a quantum quench. We verify this conclusion by investigating the Wilson loop expectation value and topological entanglement entropy. Our results suggest that the two dimensional topological quantum memory can be dynamically robust at zero temperature.

Quantifying quantum non-Markovianity based on quantum coherence via skew information

Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on $l_1$ norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative $alpha$ entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative $alpha$ entropy of coherence are more comfortable than the original Tsallis relative $alpha$ entropy of coherence for small $alpha$.

Topological band theory for non-Hermitian systems from the Dirac equation

We identify and investigate two classes of non-Hermitian systems, i.e., one resulting from Lorentz-symmetry violation (LSV) and the other from a complex mass (CM) with Lorentz invariance, from the perspective of quantum field theory. The mechanisms to break, and approaches to restore, the bulk-boundary correspondence in these two types of non-Hermitian systems are clarified. The non-Hermitian system with LSV shows a non-Hermitian skin effect, and its topological phase can be characterized by mapping it to the Hermitian system via a non-compact $U(1)$ gauge transformation. In contrast, there exists no non-Hermitian skin effect for the non-Hermitian system with CM. Moreover, the conventional bulk-boundary correspondence holds in this (CM) system. We also consider a general non-Hermitian system in the presence of both LSV and CM, and we generalize its bulk-boundary correspondence.

Characterization of topological states via dual multipartite entanglement

We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a $mathbf{Z}$ symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.

Experimental valley qubit state tomography and coherence induced uncertainty relations in monolayer WSe$_2$

Velleytronics as a new electronic conception is an emerging exciting research field with wide potential applications, which is attracting great research interests for their extraordinary properties. The localized electronic spins by optical generation of valley polarization with spin-like quantum numbers are promising candidates for implementing quantum-information processing in solids. It is expected that a single qubit preparation can be realized optically by using combination of left- and right-circularly polarized lights. Significantly in a series of experiments, this has already been well achieved by linearly polarized laser representing equal weights of left- and right-circular components resulting in formation of a valley exciton as a specific pseudo-spin qubit with equal amplitudes for spin up and spin down. Further researches on the control of valley pseudospin using longitudinal magnetic field and optical Stark effect have been reported. However, a general qubit preparation has not yet been demonstrated. Moreover as a platform for quantum information processing, the precise readout of a qubit state is necessary, for which the state tomography is a standard method in obtaining all information of a qubit state density matrix.

One-way deficit and quantum phase transitions in $XY$ model and extended Ising model

Originating in questions regarding work extraction from quantum systems coupled to a heat bath, quantum deficit, a kind of quantum correlations besides entanglement and quantum discord, links quantum thermodynamics with quantum correlations. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the $XY$ model and its extend model: the extended Ising model. We find that the one-way deficit susceptibility is able to characterize the quantum phase transitions in the $XY$ model and even the topological phase transitions in the extend Ising model. This study may enlighten extensive studies of quantum phase transitions from the perspective of quantum information processing and quantum computation, including finite-temperature phase transitions, topological phase transitions and dynamical phase transitions of a variety of quantum many-body systems.

Experimental testing of entropic uncertainty relations with multiple measurements in pure diamond

One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of quantum information, the uncertainty principle can be formulated as entropic uncertainty relations with two measurements for a quantum bit (qubit) in two-dimensional system. New entropic uncertainty relations are studied for a higher-dimensional quantum state with multiple measurements, the uncertainty bounds can be tighter than that expected from two measurements settings and cannot result from qubits system with or without a quantum memory. Here we report the first room-temperature experimental testing of the entropic uncertainty relations with three measurements in a natural three-dimensional solid-state system: the nitrogen-vacancy center in pure diamond. The experimental results confirm the entropic uncertainty relations for multiple measurements. Our result represents a more precise demonstrating of the fundamental uncertainty principle of quantum mechanics.

Majorization relation in quantum critical systems

The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the