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Register a new userTighter constraints of multiqubit entanglement for negativity
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We provide a characterization of multiqubit entanglement monogamy and polygamy constraints in terms of negativity. Using the square of convex-roof extended negativity (SCREN) and the Hamming weight of the binary vector related to the distribution of subsystems proposed in Kim (Phys Rev A 97: 012334, 2018), we provide a new class of monogamy inequalities of multiqubit entanglement based on the $alpha$th power of SCREN for $alphageq1$ and polygamy inequalities for $0leqalphaleq1$ in terms of squared convex-roof extended negativity of assistance (SCRENoA). For the case $alpha<0$, we give the corresponding polygamy and monogamy relations for SCREN and SCRENoA, respectively. We also show that these new inequalities give rise to tighter constraints than the existing ones.
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Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-$q$ entanglement and R{e}nyi-$alpha$ entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.
We introduce a feasible method of constructing the entanglement witness that detects the genuine entanglement of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are broadly theoretically and experimentally investigated. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.
We introduce a homology-based technique for the analysis of multiqubit state vectors. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown.
Entanglement plays a central role in quantum information processing, indicating the non-local correlation of quantum matters. However, few effective ways are known to detect the amount of entanglement of an unknown quantum state. In this work, we propose a scheme to estimate the entanglement negativity of any bi-partition of a composite system. The proposed scheme is based on the random unitary evolution and local measurements on the single-copy quantum states, which is more practical compared with former methods based on collective measurements on many copies of the identical state. Meanwhile, we generalize the scheme to quantify the total multi-partite correlation. We demonstrate the efficiency of the scheme with theoretical statistical analysis and numerical simulations. The proposed scheme is quite suitable for state-of-the-art quantum platforms, which can serve as not only a useful benchmarking tool to advance the quantum technology, but also a probe to study fundamental quantum physics, such as the entanglement dynamics.
In this paper, we study the monogamy inequality of Tsallis-q entropy entanglement. We first provide an analytic formula of Tsallis-q entropy entanglement in two-qubit systems for $frac{5-sqrt{13}}{2}leq qleqfrac{5+sqrt{13}}{2}.$ The analytic formula of Tsallis-q entropy entanglement in $2otimes d$ system is also obtained and we show that Tsallis-q entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis-q entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.
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