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Monogamy of entanglement is the fundamental property of quantum systems. By using two new entanglement measures based on dual entropy, the $S^{t}$-entropy entanglement and $T^{t}_q$-entropy entanglement measures, we present the general monogamy relations in multi-qubit quantum systems. We show that these newly derived monogamy inequalities are tighter than the existing ones. Based on these general monogamy relations, we construct the set of multipartite entanglement indicators for $N$-qubit states, which are shown to work well even for the cases that the usual concurrence-based indicators do not work. Detailed examples are presented to illustrate our results., Comment: 10 pages, 7 figures

The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. We propose a unified approach that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no-signaling correlations. We offer a straightforward method to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. We finally apply the lifting method to verify the correlations derived from quantum networks.

Thermodynamics as a fundamental branch of physics examines the relationships between heat, work, and energy. The maximum energy extraction can be characterized by using the passive states that has no extracted energy under any cyclic unitary process. In this paper, we focus on the concept of marginal passive state energy and derive polygon inequalities for multi-qubit entangled pure states. We show that the marginal passive state energies collectively form a convex polytope for each class of quantum states that are equivalent under SLOCC. We finally introduce multipartite passive state energy criteria to classify multipartite entanglement under SLOCC. The present result provides a thermodynamic method to witness multipartite entanglement., Comment: 7 pages. We have corrected the abstract. arXiv admin note: text overlap with arXiv:2406.13319

The presence of quantum multipartite entanglement implies the existence of a thermodynamic quantity known as the ergotropic gap, which is defined as the difference between the maximal global and local extractable works from the system. We establish a direct relation between the geometric measure of entanglement and the ergotropic gaps. We show that all the marginal ergotropic gaps form a convex polytope for each class of quantum states that are equivalent under stochastic local operations and classical communication (SLOCC). We finally introduce the concept of multipartite ergotropic gap indicators and use them to present a refined criterion for classifying entanglement under SLOCC., Comment: 7 pages (to be published)

We present the uncertainty relations in terms of the symmetrized \r{ho}-absolute variance, which generalizes the uncertainty relations for arbitrary operator (not necessarily Hermitian) to quantum channels. By recalling the quantity |U\r{ho}|({\Phi}) proposed by Zhang et al. (Quantum Inf. Process. 22 456, 2023), which involves terms of more quantum mechanical nature. We also establish the tighter uncertainty relations for quantum channels by using Cauchy-Schwarz inequality. Detailed examples are provided to illustrate the tightness of our results., Comment: 15pages, 4 figures

Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.

Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the $l_2$ norm coherence, conditional von Neumann entropy and Wigner-Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise.

The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices, from which a family of separability criteria are presented for both bipartite and multipartite systems. Moreover, new lower bounds of concurrence and convex-roof extended negativity are derived. Criteria are also given to detect the genuine tripartite entanglement. Lower bounds of the concurrence of genuine tripartite entanglement are presented. By detailed examples we show that our results are better than the corresponding ones in identifying and estimating quantum entanglement as well as genuine multipartite entanglement., Comment: 11pages, 5 figures and 2 tables

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, as well as the lower bounds of concurrence. We show by detailed examples that our separability criteria, entanglement witnesses and lower bounds can detect and estimate the quantum entanglement better than the related existing results., Comment: 16 pages,2 figures

Variational quantum circuits are one of the promising ways to exploit the advantages of quantum computing in the noisy intermediate-scale quantum technology era. The design of the quantum circuit architecture might greatly affect the performance capability of the quantum algorithms. The quantum architecture search is the process of automatically designing quantum circuit architecture, aiming at finding the optimal quantum circuit composition architecture by the algorithm for a given task, so that the algorithm can learn to design the circuit architecture. Compared to manual design, quantum architecture search algorithms are more effective in finding quantum circuits with better performance capabilities. In this paper, based on the deep reinforcement learning, we propose an approach for quantum circuit architecture search. The sampling of the circuit architecture is learnt through reinforcement learning based controller. Layer-based search is also used to accelerate the computational efficiency of the search algorithm. Applying to data classification tasks we show that the method can search for quantum circuit architectures with better accuracies. Moreover, the circuit has a smaller number of quantum gates and parameters., Comment: Comments are welcome

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures., Comment: 10 pages, 5 figures

Quantum batteries have significant potential applications for future industry and daily life. The capacity is an important indicator for a battery. Methods to improve the capacity of quantum batteries are important. We consider quantum batteries given by bipartite quantum systems and study the enhancement of the battery capacity under local projective measurements on a subsystem of the quantum state. By using two-qubit Bell-diagonal states and X-type states as examples, we show that quantum battery capacity with respect to the whole system or a subsystem can be improved by local projective measurements. Our theoretical analysis will provide ideas for the experimental development of quantum batteries., Comment: 7 pages, 3 figures

We investigate the trade-off relations between imaginarity and mixedness in arbitrary $d$-dimensional quantum systems. For given mixedness, a quantum state with maximum imaginarity is defined to be a "maximally imaginary mixed state" (MIMS). By using the $l_{1}$ norm of imaginarity and the normalized linear entropy, we conclusively identify the MIMSs for both qubit and qutrit systems. For high-dimensional quantum systems, we present a comprehensive class of MIMSs, which also gives rise to complementarity relations between the $1$-norm of imaginarity and the $1$-norm of mixedness, as well as between the relative entropy of imaginarity and the von Neumann entropy. Furthermore, we examine the evolution of the trade-off relation for single-qubit states under four specific Markovian channels: bit flip channel, phase damping channel, depolarizing channel and amplitude damping channel., Comment: 14 pages, 1 figure

Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using $\rho$-absolute variance, we introduce the uncertainty of quantum channels and explore its properties. By using Cauchy-Schwarz inequality and the parallelogram law, we establish the product and summation forms of the uncertainty relations for arbitrary two quantum channels, respectively. The summation form of the uncertainty inequalities based on the $\rho$-absolute variance for arbitrary $N$ quantum channels are also investigated and the optimal lower bounds are presented. We illustrate our results by several typical examples.

Quantum nonlocality as a witness of entanglement plays a crucial role in various fields. Existing quantum monogamy relations rule out the possibility of simultaneous violations of any Bell inequalities with partial statistics generated from one Bell experiment on any multipartite entanglement or post-quantum sources. In this paper, we report an efficient method to construct multipartite Bell test based on any Bell inequalities. We demonstrate that violating these monogamy relations can dynamically witness simultaneous Bell nonlocalities of partial systems. We conduct a tripartite experiment to verify quantum nonlocalities by violating a tripartite monogamy relation using a maximally entangled two-photon state., Comment: Maintext is included. SI is included in the published version (open access)

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.

Bell nonlocality is the key quantum resource in some device-independent quantum information processing. It is of great importance to study the efficient sharing of this resource. Unsharp measurements are widely used in sharing the nonlocality of an entangled state shared among several sequential observers. Recently, the authors in [Phys. Rev. Lett.129, 230402(2022)] showed that the Bell nonlocality of two-qubit pure states can be shared even when one only uses projective measurements and local randomness. We demonstrate that projective measurements are also sufficient for sharing the Bell nonlocality of arbitrary high-dimensional pure bipartite states. Our results promote further understanding of the nonlocality sharing of high-dimensional quantum states under projective measurements., Comment: 5 pages, 3 figures

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality are turned out to be convex. Whether nonconvex entanglement measures obeys the monogamy inequalities remains less known at present. As a well known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the $\alpha$th-power ($\alpha\geq 4\ln2$) of LCREN, and polygamy inequalities utilizing the $\alpha$th-power ($0 \leq \alpha \leq 2$) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions., Comment: 14 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1801.09882 by other authors