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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. [ABSTRACT FROM AUTHOR]

Quantum coherence, quantum entanglement and quantum nonlocality are important resources in quantum information processing. However, decoherence happens when a quantum system interacts with the external environments. We study the dynamical evolution of the three-qubit GHZ-like states in noninertial frame when one and/or two qubits undergo decoherence. Under the amplitude damping channel, we show that the quantum decoherence and the Unruh effect may have quite different influences on the initial state. Moreover, the genuine tripartite entanglement and the quantum coherence may suffer sudden death during the evolution. The quantum coherence is most resistant to the quantum decoherence and the Unruh effect and then comes the quantum entanglement and the quantum nonlocality which is most fragile among the three. The results provide a new research perspective for relativistic quantum informatics. [ABSTRACT FROM AUTHOR]

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states. [ABSTRACT FROM AUTHOR]

Quantum entanglement is the core resource in quantum information processing and quantum computing. It is a significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented by Elben et al. (Phys Rev Lett 125:200501, 2020) based on the first three partially transposed (PT) moments of density matrices. Then, Yu et al. (Phys Rev Lett 127:060504, 2021) proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement. [ABSTRACT FROM AUTHOR]

Establishing quantum correlations between two remote parties by sending an information carrier is an essential step of many protocols in quantum information processing. We obtain trade-off relations between discords and coherence within a bipartite system. Then we study the distribution of coherence in a bipartite quantum state by using the relations of relative entropy and mutual information. We show that the increase of the relative entropy of discord between two remote parties is bounded by the nonclassical correlations quantified by the relative entropy of coherence between the carrier and two remote parties, providing an optimal protocol for discord distribution and showing that quantum correlations are the essential resource for such tasks. [ABSTRACT FROM AUTHOR]

The Holevo quantity and the SU(2)-invariant states have particular importance in quantum information processing. We calculate analytically the Holevo quantity for bipartite systems composed of spin-j and spin- 1 2 subsystems with SU(2) symmetry, when the projective measurements are performed on the spin- 1 2 subsystem. The relations among the Holevo quantity, the maximal values of the Holevo quantity and the states are analyzed in detail. In particular, we show that the Holevo quantity increases in the parameter region F < Fd and decreases in region F > Fd when j increases, where F is function of temperature in thermal equilibrium and Fd = j/(2j + 1), and the maximum value of the Holevo quantity is attained at F = 1 for all j. Moreover, when the dimension of system increases, the maximal value of the Holevo quantity decreases. [ABSTRACT FROM AUTHOR]

We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems C d ⊗ C d ⊗ C d (d ≥ 3) and C d ⊗ C d + 1 ⊗ C d + 2 (d ≥ 3) . Then for general tripartite quantum system C n 1 ⊗ C n 2 ⊗ C n 3 (3 ≤ n 1 ≤ n 2 ≤ n 3) , we obtain 2 (n 2 + n 3 - 1) - n 1 nonlocal orthogonal product states. Finally, we put forward a new construction approach in C d 1 ⊗ C d 2 ⊗ ⋯ ⊗ C d n (d 1 , d 2 , ⋯ d n ≥ 3 , n > 6) multipartite systems. Remarkably, our indistinguishable sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing. [ABSTRACT FROM AUTHOR]

The detection and quantification of quantum coherence play significant roles in quantum information processing. We present an efficient way of tomographic witnessing for both theoretical and experimental detection of coherence. We prove that a coherence witness is optimal if and only if all of its diagonal elements are zero. Naturally, we obtain a bona fide homographic measure of coherence given by the sum of the absolute values of the real and the imaginary parts of the non-diagonal entries of a density matrix, together with its interesting relations with other coherence measures like l 1 norm coherence and robust of coherence. [ABSTRACT FROM AUTHOR]

Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two- and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any k ≥ 2 . The non-existence of a class of IrMOAs is also proved. [ABSTRACT FROM AUTHOR]

Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis relative operator entropy. Shannon inequality and its reverse one in Hilbert space operators derived by Furuta [Linear Algebra Appl. 381 (2004) 219] are extended in terms of the parameter of the Tsallis relative operator entropy. These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence and include some existing coherence measures as special cases. Detailed examples are given to show the relations among the measures of quantum coherence. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the μ-th power of the entanglement measure based on Rényi-α entropy, as well as polygamy relations in terms of the μ-th power of Rényi-α entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones. [ABSTRACT FROM AUTHOR]

Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here, we consider the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show that the concurrence of a pure state in any high-dimensional multipartite system can be equivalently represented by these overlaps. Here, we consider the projections of an arbitrary high-dimensional multipartite state to two-qubit states. We investigate the non-localities of these projected two-qubit sub-states by their violations of CHSH inequalities. From these violations, the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequality, we show that the concurrence of a high-dimensional multipartite pure state can be exactly expressed by these overlaps. We further derive a lower bound of the concurrence for any quantum states, which is tight for pure states. The lower bound not only imposes restriction on the non-locality distributions among the pairwise-qubit states, but also supplies a sufficient condition for distillation of bipartite entanglement. Effective criteria for detecting genuine tripartite entanglement and the lower bound of concurrence for genuine tripartite entanglement are also presented based on such non-localities. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays significant roles in quantum information processing. Estimating quantum entanglement is an essential and difficult problem in the theory of quantum entanglement. We study two main measures of quantum entanglement: concurrence and convex-roof extended negativity. Based on the improved separability criterion from the Bloch representation of density matrices, we derive analytical lower bounds of the concurrence and the convex-roof extended negativity for arbitrary dimensional bipartite quantum systems. We show that these bounds are better than some of the existing ones by detailed examples. [ABSTRACT FROM AUTHOR]

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. General monogamy relations are presented for the α th (0 ≤ α ≤ γ , γ ≥ 2) power of quantum correlation, and general polygamy relations are given for the β th (β ≥ δ , 0 ≤ δ ≤ 1) power of quantum correlation. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of α and β . Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given. [ABSTRACT FROM AUTHOR]

Monogamy and polygamy are the most striking features of the quantum world. We investigate the monogamy and polygamy relations satisfied by all quantum correlation measures for arbitrary multipartite quantum states. By introducing residual quantum correlations, analytical polygamy inequalities are presented, which are shown to be tighter than the existing ones. Then, similar to polygamy relations, we obtain strong monogamy relations that are better than all the existing ones. Typical examples are presented for illustration. [ABSTRACT FROM AUTHOR]

We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the α th ( 0 ≤ α ≤ 2 ) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the α th ( 0 ≤ α ≤ 2 ) power of concurrence for N-qubit pure states under the partition AB and C 1 ⋯ C N - 2 , as well as under the partition A B C 1 and C 2 ⋯ C N - 2 . These inequalities give rise to the restrictions on entanglement distribution and the trade-off of entanglement among the subsystems. Similar results are also derived for negativity. [ABSTRACT FROM AUTHOR]

Originating from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind of important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while it cannot be enhanced for some other cases. For coherence-breaking channels with different types, the channel distinguishability cannot be enhanced via entanglement. [ABSTRACT FROM AUTHOR]

We investigate the quantum phase transitions for the spin-1/2 chains via the quantum correlations between the nearest and next-to-nearest neighbor spins characterized by negativity, information deficit, trace distance discord and local quantum uncertainty. It is shown that all these correlations exhibit the quantum phase transitions at . However, only information deficit and local quantum uncertainty can demonstrate quantum phase transitions at . The analytical and numerical behaviors of the quantum correlations for the system are presented. We also consider quantum correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick (LMG) model. [ABSTRACT FROM AUTHOR]

We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover, two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased. [ABSTRACT FROM AUTHOR]

We study mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ . A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$ from MUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$ and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$ from MUUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0

We systematically study the construction of mutually unbiased bases in $\mathbb {C}^{2}\bigotimes \mathbb {C}^{3}$, such that all the bases are unextendible maximally entangled ones. Necessary conditions of constructing a pair of mutually unbiased unextendible maximally entangled bases in $\mathbb {C}^{2}\bigotimes \mathbb {C}^{3}$ are derived. Explicit examples are presented. [ABSTRACT FROM AUTHOR]

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability. [ABSTRACT FROM AUTHOR]

Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the l1-norm measure of coherence for convex combination of arbitrary n pure states of a quantum state ρ. Furthermore, we present triangle-like inequality for the convex-roof extended negativity for any states of rank 2, which gives a positive answer to a conjecture raised in Dai et al. (Phys. Rev. A 96:062308, 2017). Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities. [ABSTRACT FROM AUTHOR]