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Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure states is solved. For mixed states, however, the verification of local unitary equivalence is still a challenging problem. In this paper, based on the coefficient matrices of generalized Bloch representations of quantum states, we find a variety of local unitary invariants for arbitrary-dimensional bipartite quantum states. These invariants are operational and can be used as necessary conditions for verifying the local unitary equivalence of two quantum states. Furthermore, we extend the construction to the arbitrary-dimensional multipartite case. We finally apply these invariants to estimate concurrence, a vital entanglement measure, showing the practicability of local unitary invariants in characterizing entanglement.

Hardy's paradox provides an all-versus-nothing fashion to directly certify that quantum mechanics cannot be completely described by local realistic theory. However, when considering potential imperfections in experiments, like imperfect entanglement source and low detection efficiency, the original Hardy's paradox may induce a rather small Hardy violation and only be realized by expensive quantum systems. To overcome this problem, we propose a realigned Hardy's paradox. Compared with the original version of Hardy's paradox, the realigned Hardy's paradox can dramatically improve the Hardy violation. Then, we generalize the realigned Hardy's paradox to arbitrary even $n$ dichotomic measurements. For $n=2$ and $n=4$ cases, the realigned Hardy's paradox can achieve Hardy values $P(00|A_1B_1)$ approximate $0.4140$ and $0.7734$ respectively compared with $0.09$ of the original Hardy's paradox. Meanwhile, the structure of the realigned Hardy's paradox is simpler and more robust in the sense that there is only one Hardy condition rather than three conditions. One can anticipate that the realigned Hardy's paradox can tolerate more experimental imperfections and stimulate more fascinating quantum information applications., Comment: 7 pages, 1 figure

Design of detection strategies for multipartite entanglement stands as a central importance on our understanding of fundamental quantum mechanics and has had substantial impact on quantum information applications. However, accurate and robust detection approaches are severely hindered, particularly when the number of nodes grows rapidly like in a quantum network. Here we present an exquisite procedure that generates novel entanglement witness for arbitrary targeted state via a generic and operational framework. The framework enjoys a systematic and high-efficient character and allows to substantiate genuine multipartite entanglement for a variety of states that arise naturally in practical situations, and to dramatically outperform currently standard methods. With excellent noise tolerance, our framework should be broadly applicable to witness genuine multipartite entanglement in various practically scenarios, and to facilitate making the best use of entangled resources in the emerging area of quantum network., Comment: 27 pages, 5 figures

Self-testing is a device-independent examination of quantum devices based on correlations of observed statistics. Motivated by elegant progresses on self-testing strategies for measurements [Phys. Rev. Lett. 121, 250507 (2018)] and for states [New J. Phys. 20, 083041 (2018)], we develop a general self-testing procedure for multipartite generalized GHZ-state measurements. The key step is self-testing all measurement eigenstates for a general N-qubit multipartite GHZ-state measurement. Following our procedure, one only needs to perform local measurements on N-2 chosen parties of the N-partite eigenstate and maintain to achieve the maximal violation of tilted Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for remaining two parties. Moreover, this approach is physically operational from an experimental point of view. It turns out that the existing result for three-qubit GHZ-state measurement is recovered as a special case. Meanwhile, we develop the self-testing method to be robust against certain white noise.

Graph states -- one of the most representative families of multipartite entangled states, are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in the quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states, by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and linear cluster states achieve a high degree of Bell violation, which are beyond the nontrivial bounds of the robust self-testing scheme. Furthermore, our work paves the way to the device-independent certification of complex multipartite quantum states.

Quantum cryptographic conferencing (QCC) holds promise for distributing information-theoretic secure keys among multiple users over long distance. Limited by the fragility of Greenberger-Horne-Zeilinger (GHZ) state, QCC networks based on directly distributing GHZ states at long distance still face big challenge. Another two potential approaches are measurement device independent QCC and conference key agreement with single-photon interference, which was proposed based on the post-selection of GHZ states and the post-selection of W state, respectively. However, implementations of the former protocol are still heavily constrained by the transmission rate $\eta$ of optical channels and the complexity of the setups for post-selecting GHZ states. Meanwhile, the latter protocol cannot be cast to a measurement device independent prepare-and-measure scheme. Combining the idea of post-selecting GHZ state and recently proposed twin-field quantum key distribution protocols, we report a QCC protocol based on weak coherent state interferences named phase-matching quantum cryptographic conferencing, which is immune to all detector side-channel attacks. The proposed protocol can improve the key generation rate from $\mathrm{O}(\eta^N)$ to $\mathrm{O}(\eta^{N-1})$ compared with the measurement device independent QCC protocols. Meanwhile, it can be easily scaled up to multiple parties due to its simple setup.