Bell's Inequality and Entanglement in Qubits

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.Comment: 10 page

Evolution of entanglement spectra under generic quantum dynamics

We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct timescales. First, on an o(1) timescale, independent of system or subsystem size and the details of the dynamics, the entanglement spectrum develops nearest-neighbor level repulsion. The second timescale sets in when the light-cone has traversed the subsystem. Between these two times, the density of states of the reduced density matrix takes a universal, scale-free 1/f form; thus, random-matrix theory captures the local statistics of the entanglement spectrum but not its global structure. The third time scale is that on which the entanglement saturates; this occurs well after the light-cone traverses the subsystem. Between the second and third times, the entanglement spectrum compresses to its thermal Marchenko-Pastur form. These features hold for chaotic Hamiltonian and Floquet dynamics as well as a range of quantum circuit models.Comment: 12 pages, 15 figure

Distributionally Robust Semi-Supervised Learning for People-Centric Sensing

Semi-supervised learning is crucial for alleviating labelling burdens in people-centric sensing. However, human-generated data inherently suffer from distribution shift in semi-supervised learning due to the diverse biological conditions and behavior patterns of humans. To address this problem, we propose a generic distributionally robust model for semi-supervised learning on distributionally shifted data. Considering both the discrepancy and the consistency between the labeled data and the unlabeled data, we learn the latent features that reduce person-specific discrepancy and preserve task-specific consistency. We evaluate our model in a variety of people-centric recognition tasks on real-world datasets, including intention recognition, activity recognition, muscular movement recognition and gesture recognition. The experiment results demonstrate that the proposed model outperforms the state-of-the-art methods.Comment: 8 pages, accepted by AAAI201