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We present a nonlinear entanglement detection strategy which detects entanglement that the linear detection strategy fails. We show that when the nonlinear entanglement detection strategy fails to detect the entanglement of an entangled state with two copies, it may succeed with three or more copies. Based on our strategy, a witness combined with a suitable quanutm mechanical observable may detect the entanglement that can not be detected by the witness alone. Moreover, our strategy can also be applied to detect multipartite entanglement by using the witnesses for bipartite systems, as well as to entanglement concentrations., Comment: 13 pages, 5 figures

The distribution relationship of quantum battery capacity is investigated. First, it is proved that for two-qubit X-states, the sum of the subsystem battery capacities does not exceed the total system's battery capacity, and the conditions are provided under which they are equal. Then define the difference between the total system's and subsystems'battery capacities as the residual battery capacity (RBC) and show that this can be divided into coherent and incoherent components. Furthermore, it is observed that this capacity monogamy relation for quantum batteries extends to general n-qubit X states and any n-qubit X state's battery capacity distribution can be optimized to achieve capacity gain through an appropriate global unitary evolution. Specifically, for general three-qubit X states, stronger distributive relations are derived for battery capacity. Quantum batteries are believed to hold significant potential for outperforming classical counterparts in the future. These findings contribute to the development and enhancement of quantum battery theory., Comment: 11 pages, 5 figures

Wu et al. [J. High Energ. Phys. 2023, 232 (2023)] first found that the fidelity of quantum teleportation with a bipartite entangled resource state, completely determined by the fully entangled fraction (FEF) characterized by the maximal fidelity between the given quantum state and the set of maximally entangled states, can monotonically increase in Schwarzschild spacetime. We investigated the Hawking effect on the FEF of quantum states in tripartite systems. In this paper, we show that the Hawking effect of a black hole may both decrease and increase the FEF in Schwarzschild spacetime. For an initial X-type state, we found that the Hawking effect of the black hole has both positive and negative impacts on the FEF of Dirac fields, depending on the selection of initial states. For an initial W-like state, the Hawking effect of the black hole has only a positive impact on the FEF of Dirac fields, independent of the selection of initial states. Our results provide an insightful view of quantum teleportation in multipartite systems under the influence of Hawking effects, from the perspective of quantum information and general relativity., Comment: 10 pages, 5 figures, 3 tables

Entanglement is fundamental inasmuch because it rephrases the quest for the classical-quantum demarcation line, and it also has potentially enormous practical applications in modern information technology. In this work, employing the approach of matrix decomposition, we introduce and formulate a practicable criterion for separability based on the correlation tensor. It is interesting that this criterion unifies several relevant separability criteria proposed before, even stronger than some of them. Theoretical analysis and detailed examples demonstrate its availability and feasibility for entanglement detection. Furthermore we build a family of entanglement witnesses using the criterion according to its linearity in the density operator space.

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

As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separablity [Phys. Rev. Lett. {\bf 127}, 060504 (2021)], we propose two sets of separability criteria using moments of the correlation tensor for bipartite and multipartite quantum states, which are shown to be stronger in some aspects of detecting entanglement., Comment: 12pp

Quantum Bell nonlocality is an important quantum phenomenon. Recently, the shareability of Bell nonlocality under unilateral measurements has been widely studied. In this study, we consider the shareability of quantum Bell nonlocality under bilateral measurements. Under a specific class of projection operators, we find that quantum Bell nonlocality cannot be shared for a limited number of times, as in the case of unilateral measurements. Our proof is analytical and our measurement strategies can be generalized to higher dimension cases., Comment: 15 pages

We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes., Comment: 8 pages; no figure

Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We shaw that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.

In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous lower bounds. We then propose new weighted uncertainty relations for two noncompatible observables. Two separable criteria via skew information are also obtained., Comment: 11pages

The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence., Comment: 5 pages

We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy Schwarz inequality., Comment: 6 pages,1 figure

We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be extended to multipartite high dimensional system., Comment: 10pages

We study the trade-off relations on the maximal violation of CHSH tests for the multi-qubit pure states. Firstly, according to the classification of 3-qubit pure states under stochastic local operations and classical communication, four trade-off relations on CHSH tests are provided. The process of proof also provides the method of calculating its exact value. Then we consider the multi-qubit quantum systems, and we prove that the conjecture in [PRA 94, 042105 (2016)] is right for some special 4-qubit or more qubit pure states., Comment: 10pages

We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement., Comment: 6 pages

We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their coefficient matrices. This condition can be used to classify some SLOCC equivalent quantum states with coefficient matrices having the same rank. For multipartite mixed state, we provide a necessary and sufficient condition by means of the realignment of matrix. Some detailed examples are given to identify the SLOCC equivalence of multipartite quantum states.

We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT., Comment: 9 pages

We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact approximation of a density matrices by tensor product of positive semi-definite operators is determined by the additivity property of the density matrix., Comment: 8 pages

We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands., Comment: 13 pages