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Zhiwei Song

Publications and source records attributed to Zhiwei Song.

13 recordsLinked to original sources

A partial-trace matrix inequality and Werner-state distillability

Motivated by the equivalent partial-trace formulations of Werner-state distillability [P. Costa Rico, Lett. Math. Phys. 115, 47 (2025); S.-Y. Qi et al., Phys. Rev. A 110, 012406 (2024)], we prove a bipartite partial-trace inequality for every matrix of rank at most two. As applications, we prove the two-copy undistillability of NPT Werner states in arbitrary local dimension, thereby resolving this open problem highlighted in [P. Horodecki et al., PRX Quantum 3, 010101 (2022)]. We further prove a two-parameter extension of the matrix inequality and show that two individually one-copy-undistillable NPT Werner states cannot activate each other's one-copy distillability. We also resolve the singular-value maximization problem associated with the two-ququart case.

quant-ph

A counterexample to the strong spin alignment conjecture

The spin alignment conjecture was originally formulated in connection with the additivity of coherent information for a class of quantum channels known as platypus channels. Recently, a stronger majorization-based version was proposed by M. A. Alhejji and E. Knill [Commun. Math. Phys. 405, 119, 2024], asserting that the spectrum of the alignment operator is always majorized by that of the perfectly aligned configuration. In this letter, we show that this strong spin alignment conjecture is false in general by constructing an explicit counterexample in the smallest unresolved case, namely three qubits. The example uses two-body states that are not jointly compatible with any single three-qubit global state, which naturally leads to a compatibility-constrained variant of the conjecture.

quant-ph

Extreme points of absolutely PPT states with exactly three distinct eigenvalues

Whether the sets of absolutely separable (AS) and absolutely two-qutrit positive-partial-transpose (AP) states are the same has been an open problem in entanglement theory for decades. Since they are both convex sets, we investigate the boundary and extreme points of full-rank two-qutrit AP states with exactly three distinct eigenvalues. We show that every boundary point is an extreme point, with exactly one exception. We explicitly characterize the expressions of such points, each of which turns out to contain at most one parameter in some intervals. When the parameter approaches the ends of intervals, most points become the known extreme points of exactly two distinct eigenvalues. We present our results by tables and figures.

quant-ph

Spectral characterizations of entanglement witnesses

We present a systematic investigation of the spectral properties of entanglement witnesses (EWs). Specifically, we analyze the infimum and supremum of the largest eigenvalue, the smallest eigenvalue, the negativity (defined as the absolute value of the sum of negative eigenvalues), and the squared Frobenius norm of a unit-trace (normalized) entanglement witness, along with the conditions under which these values are attained. Our study provides distinct characterizations for decomposable (DEWs) and nondecomposable entanglement witnesses (NDEWs). While these two classes share many spectral similarities, we reveal a fundamental divergence by proving that the infimum of the smallest eigenvalue can be attained by DEWs, yet remains strictly unattainable for all NDEWs. We apply the results to provide necessary conditions for an EW to possess a mirrored EW. Furthermore, we demonstrate the superior detection capability of NDEWs by proving that any non-positive-transpose (NPT) state beyond the two-qubit and qubit-qutrit systems can be detected by an NDEW.

quant-ph

Multipartite entangling power by von Neumann entropy

Quantifying the entanglement generation of a multipartite unitary operation is a key problem in quantum information processing. We introduce the definition of multipartite entangling, assisted entangling, and disentangling power, which is a natural generalization of the bipartite ones. We show that they are assumed at a specified quantum state. We analytically derive the entangling power of Schmidt-rank-two multi-qubit unitary operations by the minimal convex sum of modulo-one complex numbers. Besides we show the necessary and sufficient condition that the assisted entangling power of Schmidt-rank-two unitary operations reaches the maximum. We further investigate the widely-used multi-qubit gates, for example, the entangling and assisted entangling power of the $n$-qubit Toffoli gate is one ebit. The entangling power of the three-qubit Fredkin gate is two ebits, and that of the four-qubit Fredkin gate is in two to $\log_25$ ebits.

quant-ph

On the extreme points of sets of absolulely separable and PPT states

The absolutely separable (resp. PPT) states remain separable (resp. positive partial transpose) under any global unitary operation. We present a compact form of the extreme points in the sets of absolutely separable states and PPT states in two-qubit and qubit-qudit systems. The results imply that each extreme point has at most three distinct eigenvalues. We establish a necessary and sufficient condition for determining extreme points of the set of absolutely PPT states in two-qutrit and qutrit-qudit systems, expressed as solvable linear equations. We also demonstrate that any extreme point in qutrit-qudit system has at most seven distinct eigenvalues. We introduce the concept of robustness of nonabsolute separability. It quantifies the minimal amount by which a state needs to mix with other states such that the overall state is absolutely separable. We show that the robustness satisfies positivity, invariance under unitary transformation, monotonicity and convexity, so it is a good measure within the resource theory of nonabsolute separability. Analytical expressions for this measure are given for pure states in arbitrary system and rank-two mixed states in two-qubit system.

quant-ph

Mutually-orthogonal unitary and orthogonal matrices

We introduce the concept of n-OU and n-OO matrix sets, a collection of n mutually-orthogonal unitary and real orthogonal matrices under Hilbert-Schmidt inner product. We give a detailed characterization of order-three n-OO matrix sets under orthogonal equivalence. As an application in quantum information theory, we show that the minimum and maximum numbers of an unextendible maximally entangled bases within a real two-qutrit system are three and four, respectively. Further, we propose a new matrix decomposition approach, defining an n-OU (resp. n-OO) decomposition for a matrix as a linear combination of n matrices from an n-OU (resp. n-OO) matrix set. We show that any order-d matrix has a d-OU decomposition. As a contrast, we provide criteria for an order-three real matrix to possess an n-OO decomposition.

quant-ph

The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local operations and classical communication

We show that every three-dimensional subspace of qutrit-qudit complex or real systems has a distinguishable basis under one-way local operations and classical communication (LOCC). In particular this solves an open problem proposed in [J. Phys. A, 40, 7937, 2007]. We construct a three-dimensional space whose locally distinguishable basis is unique and apply the uniqueness property to the task of state transformation. We also construct a three-dimensional locally distinguishable multipartite space assisted with entanglement. On the other hand, we show that four-dimensional indistinguishable bipartite subspaces under one-way LOCC exist. Further, we show that the environment-assisted classical capacity of every channel with a three-dimensional environment is at least $\log_2 3$, and the environment-assisting classical capacity of any qutrit channel is $\log_2 3$. We also show that every two-qutrit state can be converted into a generalized classical state near the quantum-classical boundary by an entanglement-breaking channel.

quant-ph

Cyclegan Network for Sheet Metal Welding Drawing Translation

In intelligent manufacturing, the quality of machine translation engineering drawings will directly affect its manufacturing accuracy. Currently, most of the work is manually translated, greatly reducing production efficiency. This paper proposes an automatic translation method for welded structural engineering drawings based on Cyclic Generative Adversarial Networks (CycleGAN). The CycleGAN network model of unpaired transfer learning is used to learn the feature mapping of real welding engineering drawings to realize automatic translation of engineering drawings. U-Net and PatchGAN are the main network for the generator and discriminator, respectively. Based on removing the identity mapping function, a high-dimensional sparse network is proposed to replace the traditional dense network for the Cyclegan generator to improve noise robustness. Increase the residual block hidden layer to increase the resolution of the generated graph. The improved and fine-tuned network models are experimentally validated, computing the gap between real and generated data. It meets the welding engineering precision standard and solves the main problem of low drawing recognition efficiency in the welding manufacturing process. The results show. After training with our model, the PSNR, SSIM and MSE of welding engineering drawings reach about 44.89%, 99.58% and 2.11, respectively, which are superior to traditional networks in both training speed and accuracy.

cs.CV

Segmentation method of U-net sheet metal engineering drawing based on CBAM attention mechanism

In the manufacturing process of heavy industrial equipment, the specific unit in the welding diagram is first manually redrawn and then the corresponding sheet metal parts are cut, which is inefficient. To this end, this paper proposes a U-net-based method for the segmentation and extraction of specific units in welding engineering drawings. This method enables the cutting device to automatically segment specific graphic units according to visual information and automatically cut out sheet metal parts of corresponding shapes according to the segmentation results. This process is more efficient than traditional human-assisted cutting. Two weaknesses in the U-net network will lead to a decrease in segmentation performance: first, the focus on global semantic feature information is weak, and second, there is a large dimensional difference between shallow encoder features and deep decoder features. Based on the CBAM (Convolutional Block Attention Module) attention mechanism, this paper proposes a U-net jump structure model with an attention mechanism to improve the network's global semantic feature extraction ability. In addition, a U-net attention mechanism model with dual pooling convolution fusion is designed, the deep encoder's maximum pooling + convolution features and the shallow encoder's average pooling + convolution features are fused vertically to reduce the dimension difference between the shallow encoder and deep decoder. The dual-pool convolutional attention jump structure replaces the traditional U-net jump structure, which can effectively improve the specific unit segmentation performance of the welding engineering drawing. Using vgg16 as the backbone network, experiments have verified that the IoU, mAP, and Accu of our model in the welding engineering drawing dataset segmentation task are 84.72%, 86.84%, and 99.42%, respectively.

cs.CV

A complete picture of the four-party linear inequalities in terms of the 0-entropy

Multipartite quantum system is complex. Characterizing the relations among the three bipartite reduced density operators $\rho_{AB}$, $\rho_{AC}$ and $\rho_{BC}$ of a tripartite state $\rho_{ABC}$ has been an open problem in quantum information. One of such relations has been reduced by [Cadney et al, LAA. 452, 153, 2014] to a conjectured inequality in terms of matrix rank, namely $r(\rho_{AB}) \cdot r(\rho_{AC})\ge r(\rho_{BC})$ for any $\rho_{ABC}$. It is denoted as open problem $41$ in the website "Open quantum problems-IQOQI Vienna". We prove the inequality, and thus establish a complete picture of the four-party linear inequalities in terms of the $0$-entropy. Our proof is based on the construction of a novel canonical form of bipartite matrices under local equivalence. We apply our result to the marginal problem and the extension of inequalities in the multipartite systems, as well as the condition when the inequality is saturated.

quant-ph

Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates

It is known that every two-qubit unitary operation has Schmidt rank one, two or four, and the construction of three-qubit unitary gates in terms of Schmidt rank remains an open problem. We explicitly construct the gates of Schmidt rank from one to seven. It turns out that the three-qubit Toffoli and Fredkin gate respectively have Schmidt rank two and four. As an application, we implement the gates using quantum circuits of CNOT gates and local Hadamard and flip gates. In particular, the collective use of three CNOT gates can generate a three-qubit unitary gate of Schmidt rank seven in terms of the known Strassen tensor from multiplicative complexity. Our results imply the connection between the number of CNOT gates for implementing multiqubit gates and their Schmidt rank.

quant-ph

Information Encoding with Optical Dielectric Metasurface via Independent Multichannels

Information encryption and security is a prerequisite for information technology which can be realized by optical metasurface owing to its arbitrary manipulation over the wavelength, polarization, phase and amplitude of light. So far information encoding can be implemented by the metasurface in one dimensional (1D) mode (either wavelength or polarization) only with several combinations of independent channels. Here we successfully apply dielectric metasurfaces in a 2D mode (both wavelength and polarization) with far more combinations of independent channels to encrypt information, which therefore enhances the encryption security dramatically. Six independent channels by two circular polarization states (RCP and LCP) and three visible wavelengths (633 nm, 532 nm and 473 nm) in 2D mode can produce 63 combinations available to information encoding, in sharp contrast with 7 combinations by 3 independent channels in 1D mode. This 2D mode encoding strategy paves a novel pathway for escalating the security level of information in multichannel information encryption, anti-counterfeiting, optical data storage, and information processing.

physics.optics