Multi-party quantum steering is an important concept in quantum information theory and quantum mechanics, typically related to quantum entanglement and quantum nonlocality. It enables precise manipulation of large quantum systems, which is essential for large-scale quantum computing, simulations, and quantum communication. Recently, a quantum steering certification for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states based on the fine-grained steering inequality was proved [Quantum Studies: Mathematics and Foundations, 2022, 9(2): 175-198]. Here we provide an experimental proposal to prepare the GGHZ states in photon system. The measurement observalbes in each party can be realized by different polarization optical elements. By choosing the angles of the waveplates, our experiment proposal can observe the maximum quantum violation for any three-qubit GGHZ states. Our proposal can be easily extended to high-dimensional qubits and multi-photon GHZ states, which provides a method to study the complex multi-party quantum protocols.

To enhance the surface protection of exposed moving parts made from magnesium alloys, this study focuses on developing high-performance micro-arc composite (MCC) coatings on AZ80 wrought magnesium alloy substrate. AZ80 alloys were fabricated through forging at different temperatures (250 °C, 350 °C, and 450 °C) to investigate the influence of thermal deformation on substrate properties. Subsequently, micro-arc oxidation (MAO) coatings and MCC coatings were applied to the forged alloys. Comprehensive analyses—including microstructural characterization, salt spray corrosion tests, and stress corrosion cracking (SCC) evaluations—were conducted under both static and stress conditions. Among the forging temperatures, 250 °C produced substrates with refined grains and a favorable distribution of β-Mg17Al12 precipitates, resulting in improved baseline corrosion resistance. MAO coatings offered moderate protection, primarily delaying corrosion initiation and crack propagation under stress environments. Building upon this foundation, MCC coatings—fabricated by electrostatic spraying to form an inner-embedded and outer-wrapped structure over the MAO layer—demonstrated significantly superior protective performance. Under both static and stress corrosion scenarios, the MCC coatings effectively suppressed SCC initiation and progression, highlighting their potential for robust surface protection in demanding service environments.

The imaginary unit i has recently been experimentally proven to be indispensable for quantum mechanics. We study the differences in detection power between real and complex entanglement witnesses (EWs) distinguished by whether their matrix expressions incorporate imaginary parts. We show that a real EW (REW), denoted by a real Hermitian matrix, must detect one entangled state of a real density matrix, and conversely an entangled state of a real density matrix must be detected by one REW. We present a necessary and sufficient condition for the entangled states detected by REWs and give a specific example implying the detection limitations of REWs. From an operational perspective, we investigate whether all entangled states are detected by the EWs locally equivalent to some REWs. We prove the validity for all nonpositive partial transpose states. We also derive a necessary and sufficient condition of the validity for the positive partial transpose (PPT) entangled states of complex density matrices. By this condition we show the validity for a family of two-qutrit PPT entangled states of rank four. Another way to figure out the problem is to check whether a counterexample exists. We propose a method to examine the existence from a set-theoretic perspective and provide some supporting evidence of nonexistence. Finally, we derive some results on local projections of EWs with product projectors.

The problem of determining whether two states are equivalent by local unitary (LU) operations is important for quantum information processing. In this paper, we propose an alternative perspective to study this problem by comparing the decidabilities of LU equivalence (also known as LU decidabilities for short) between entanglement witnesses and states. We introduce a relation between sets of Hermitian operators in terms of the LU decidability. Then, we compare the LU decidability for the set of entanglement witnesses to the LU decidabilities for several sets of states. By comparison, we establish a hierarchy of these sets in terms of LU decidabilities. Moreover, we realize that the simultaneous LU (SLU) equivalence between tuples of mutually orthogonal projectors is crucial to LU equivalent operators. We reveal by examples that for two tuples of projectors, the partial SLU equivalence cannot ensure the overall SLU equivalence. Generally, we present a necessary and sufficient condition such that two tuples of states are SLU equivalent.

Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertia of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertia of the partial transpose of the two-qutrit bipartite NPT states. As an application, we extend our results to high-dimensional states.

Efficiently detecting entanglement based on measurable quantities is a basic problem for quantum information processing. Recently, the measurable quantities called partial-transpose (PT)-moments have been proposed to detect and characterize entanglement. In the recently published paper [L. Zhang \emph{et al.}, \href{https://doi.org/10.1002/andp.202200289}{Ann. Phys.(Berlin) \textbf{534}, 2200289 (2022)}], we have already identified the 2-dimensional (2D) region, comprised of the second and third PT-moments, corresponding to two-qubit entangled states, and described the whole region for all two-qubit states. In the present paper, we visualize the 3D region corresponding to all two-qubit states by further involving the fourth PT-moment (the last one for two-qubit states). The characterization of this 3D region can finally be achieved by optimizing some polynomials. Furthermore, we identify the dividing surface which separates the two parts of the whole 3D region corresponding to entangled and separable states respectively. Due to the measurability of PT-moments, we obtain a complete and operational criterion for the detection of two-qubit entanglement.

Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on the asymmetric setting of QHT, where the two types of decision errors are treated unequally, considering the operational limitations arising from the lack of a reference frame for chirality. This reference frame is associated with the group $\bbZ_2$ consisting of the identity transformation and the parity transformation. Thus, we have to discriminate between two qubit states by performing the $\bbZ_2$-invariant POVMs only. We start from the discrimination between two pure states. By solving the specific optimization problem we completely characterize the asymptotic behavior of the minimal probability of type-II error which occurs when the null hypothesis is accepted when it is false. Our results reveal that the minimal probability reduces to zero in a finite number of copies, if the $\bbZ_2$-twirlings of such two pure states are different. We further derive the critical number of copies such that the minimal probability reduces to zero. Finally, we replace one of the two pure states with a maximally mixed state, and similarly characterize the asymptotic behavior of the minimal probability of type-II error.

The pure states that can be uniquely determined among all (UDA) states by their marginals are essential to efficient quantum state tomography. We generalize the UDA states from the context of pure states to that of arbitrary (whether pure or mixed) states, motivated by the efficient state tomography of low -rank states. The concept of additivity of k-UDA states for three different composite types of tensor product applies if the composite state of two k-UDA states is still uniquely determined by the k -partite marginals for the corresponding type of tensor product. We show that the additivity holds if one of the two initial states is pure and present the conditions under which the additivity holds for two mixed UDA states. One of the three composite types of tensor product is also adopted to construct genuinely multipartite entangled (GME) states. Therefore, it is effective to construct multipartite k-UDA states with genuine entanglement by uniting the additivity of k-UDA states and the construction of GME states.

Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states, and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states.

Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertias of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertias of the patial transpose of the two-qutrit bipartite NPT states. As an application, we extend our results to high dimensional states.

The multipartite unitary gates are called genuine if they are not product unitary operators across any bipartition. We mainly investigate the classification of genuine multipartite unitary gates of Schmidt rank two, by focusing on the multiqubit scenario. For genuine multipartite (excluding bipartite) unitary gates of Schmidt rank two, there is an essential fact that their Schmidt decompositions are unique. Based on this fact, we propose a key notion named as singular number to classify the unitary gates concerned. The singular number is defined as the number of local singular operators in the Schmidt decomposition. We then determine the accurate range of singular number. For each singular number, we formulate the parametric Schmidt decompositions of genuine multiqubit unitary gates under local equivalence. Finally, we extend the study to three-qubit diagonal unitary gates due to the close relation between diagonal unitary gates and Schmidt-rank-two unitaries. We start with discussing two typical examples of Schmidt rank two, one of which is a fundamental three-qubit unitary gate, i.e., the CCZ gate. Then we characterize the diagonal unitary gates of Schmidt rank greater than two. We show that a three-qubit diagonal unitary gate has Schmidt rank at most three, and present a necessary and sufficient condition for such a unitary gate of Schmidt rank three. This completes the characterization of all genuine three-qubit diagonal unitary gates.

The influences of the forging process and micro-arc oxidation (MAO) coating on the corrosion behavior of ZK60 wrought magnesium alloys exposed to salt spray and constant stress corrosion conditions were investigated. The microstructure of the ZK60 Mg alloy specimens forged under different temperatures (i.e., 250, 300, and 450 °C) was characterized using metallography, EBSD, and SEM. It was demonstrated that the ZK60 alloy forged at 300 °C (i.e., ZK60EF-300) had finer grain and uniformly distributed β-phase and, thus, better corrosion resistance than the ZK60 forged at 450 °C. At the lower forging temperature (250 °C) twins formed in the ZK60 alloy, which accelerated the corrosion of the ZK60E-250 specimen. The MAO coating provided robust corrosion protection for all the ZK60 wrought Mg alloy substrates. The salt spray corrosion test results showed that when the MAO coating broke down at certain weak sites, the corrosion performance of the coated Mg alloy was predominantly determined by the alloy substrate. The stress corrosion behaviors of the uncoated and MAO-coated ZK60 alloy specimens were also investigated under a constant load of 80 MPa in 3.5 wt.% NaCl solution. The MAO coating was found to improve the stress-corrosion resistance of the ZK60 alloy pronouncedly.

We study $k$ -uniform states in heterogeneous systems whose local dimensions are not all the same. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$ -uniform states, we present two constructions of 2-uniform states in heterogeneous systems. We also construct two families of 3-uniform states in heterogeneous systems, which solves a question posed in [D. Goyeneche et al., Phys. Rev. A 94, 012346 (2016)]. We show two methods of generating $(k-1)$ -uniform states from $k$ -uniform states. Some results on the nonexistence of absolutely maximally entangled states are provided. For the applications, we present an orthogonal basis consisting of $k$ -uniform states with the minimum support, and we show that some $k$ -uniform bases are locally irreducible. Moreover, we connect $k$ -uniform states with quantum information masking.

The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, asks whether such process exists. The 2-copy undistillability of 4×4 Werner states has been reduced to the validity of a conjecture for the following matrix inequality with d=4supX∈Xd⁡σ12(X)+σ22(X)⩽3d−4d2, where σ1(X) and σ2(X) are the largest two singular values of X, Xd is the set of all matrices X=A⊗I+I⊗B with A,B∈Cd×d(d⩾4), Tr(A)=Tr(B)=0 and ‖A‖F2+‖B‖F2=1/d. The latest progress, made by Pankowski et al. (2010) [21], shows that this conjecture holds when both matrices A and B are normal. In this paper, we prove that the conjecture holds when one of matrices A and B is normal and the other one is arbitrary via optimization techniques. Our work makes solid progress towards this conjecture and thus the distillability problem.

The author of the Comment [Phys. Rev. A 104, 016401 (2021)] pointed out the missing part in the proof of Theorem 20 in our work [L. Qian et al., Phys. Rev. A 99, 032312 (2019)], and presented a sufficient and necessary condition for the separability of completely symmetric (CS) states in the two-qutrit system. While being technically correct, the proposed example is still a separable CS state according to Ha's sufficient and necessary condition. We provide another proof to show that every bipartite CS state of rank five is separable. This result bridges the gap appearing in our previous proof. It turns out that every two-qutrit CS state is separable, and thus making our conclusion (Theorem 20 of our work) still valid.

For lung adenocarcinoma, arm aneuploidy landscape among primary and metastatic sites, and among different driver and frequently mutated gene groups have not been previously studied. We collected the largest cohort of LUAD patients (n=3533) to date and analyzed the profiles of chromosome arm aneuploidy (CAA), and its association with different metastatic sites and mutated gene groups. Our results showed distant metastasis (bone, brain, liver) were characterized by high CAA burden and biased towards arm losses compared to regional metastasis (pleura, chest) and primary tumors. Moreover, EGFR, MET, PIK3CA, PKHD1 and RB1 mutant groups were found to have high CAA burden, while those with BRAF, ERBB2 and KRAS mutations belonged to the low CAA burden group. Comparing EGFR L858R and EGFR 19del mutants, distinct CAA co-occurrences were observed. Network-based stratification with population based genomic evolution analysis revealed two distinct subtypes of LUAD with different CAA signatures and unique CAA order of acquisition. In summary, our study presented a comprehensive characterization of arm aneuploidy landscape and evolutionary trajectories in lung adenocarcinoma, which could provide basis for both biological and clinical investigations in the future.

Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points given by the Schmidt coefficients of the entangled source and target states. The lower bounds on the dimensions of the catalytic states are also investigated. Moreover, we give a detailed protocol of quantum mixed state transformation under entanglement-assisted LOCC.

The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\cH=\bbC^2\ox\bbC^2\ox\bbC^4$, three UPBs of size $9$ in $\cK=\bbC^4\ox\bbC^4$, and no UPB of size $7$ in $\cH$ and $\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\r$ of rank seven, and show that it is also a PPT entangled state in $\cH$ and $\cK$, respectively. We analytically derive the geometric measure of entanglement of a special $\r$.

Abstract Background: Lung adenocarcinoma (LUAD) is the most common subtype of non-small cell lung cancer. Overall aneuploidy frequency in LUAD have been previously documented. We aimed to assess whether specific chromosome arm aneuploidy (CAA) patterns can be found in primary tumor and different metastatic sites, and across patients with different driver mutations. We also investigated CAA and driver mutation co-occurrence patterns in LUAD, as well as probable order of CAA acquisition. Methods: We performed targeted panel sequencing (425 cancer-related genes) on 3533 tissue samples from LUAD patients. CAA status (arm gain or loss) was derived from segmental copy number analysis using Sequenza, accounting for purity and ploidy. 4 types of CAA analysis were conducted: total CAA burden, gain-loss pattern, co-occurrence/exclusivity, and population level CAA progression assessed by Tronco on network-based stratified (NBS) subtypes. Results: Use of panel sequencing data for analysis of CAA status was validated against WES results, and achieved high concordance (Kappa: 0.75, Pearson: 0.85). Primary tumor and different metastatic sites had dramatic differences in CAA burdens (p=3.4e-06). Liver and brain had more arm losses than gains compared to primary (q=0.047 and 0.049 respectively). Different driver mutation groups also had significant difference in CAA burden (p<2.2e-16). BRAF group had more arm gains than losses; whereas PIK3CA had more arm losses than gains. TP53 mutation status had a moderating effect on both CAA burden and gain-loss pattern across metastatic sites and driver mutation groups. EGFR 19del and L858R mutations showed significant differences in CAA co-occurrence/exclusion. EGFR 19del tend to co-occur with 4q-, 5p-, 5q-, 8q+, 9p+, 16q+, 17p+, 17q-, 22q-, and was in exclusion with 14q-. EGFR L858R co-occurred with 4q+, but was in exclusion with 1p-, 8p+ and 16p-. MET significantly co-occurred with 1q-, and PIK3CA with 2p+. Clustering of LUAD patients using NBS gave us 2 tight clusters with high silhouette score (0.86). These two LUAD subtypes showed distinct orders of CAA acquisition. Both clustered subtypes began with acquisition of 7p gain. Subtype 1 is dominated by initial arm gains, followed by few arm losses, seen in previously published literature; whereas subtype 2 began with a simultaneous acquisition of 19p loss, with further additions of many arm losses, before eventual accumulation of arm gains. Proportion of these 2 subtypes varied across primary and metastatic sites, and driver mutant groups. Conclusions: There are significant differences in arm aneuploidy patterns across metastatic sites and mutation groups. Overall, LUAD patients exhibit a unique pattern of co-occurrence and exclusivity between CAA and driver mutations, as well as two subtypes with distinct CAA evolution trajectories. These CAA patterns may hold biological meaning and may be useful predictors of clinical outcomes and warrants further investigation. Citation Format: Hua Bao, Ming Han, Yi Shen, Xue Wu, Yang Shao. Chromosome arm aneuploidy landscape in lung adenocarcinoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 2210.

We study $k$-uniform states in heterogeneous systems whose local dimensions are mixed. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$-uniform states, we present two constructions of $2$-uniform states in heterogeneous systems. We also construct a family of $3$-uniform states in heterogeneous systems, which solves a question posed in [D. Goyeneche et al., Phys. Rev. A 94, 012346 (2016)]. We also show two methods of generating $(k-1)$-uniform states from $k$-uniform states. Some new results on the existence and nonexistence of absolutely maximally entangled states are provided. For the applications, we present an orthogonal basis consisting of $k$-uniform states with minimum support. Moreover, we show that some $k$-uniform bases can not be distinguished by local operations and classical communications, and this shows quantum nonlocality with entanglement.