An entanglement measure for n-qubits

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.Comment: 16 pages, no figure

SLOCC invariant and semi-invariants for SLOCC classification of four-qubits

We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.Comment: 22 pages, no figures, 9 tables, submit the paper to a journa

Masked Image Residual Learning for Scaling Deeper Vision Transformers

Deeper Vision Transformers (ViTs) are more challenging to train. We expose a degradation problem in deeper layers of ViT when using masked image modeling (MIM) for pre-training. To ease the training of deeper ViTs, we introduce a self-supervised learning framework called Masked Image Residual Learning (MIRL), which significantly alleviates the degradation problem, making scaling ViT along depth a promising direction for performance upgrade. We reformulate the pre-training objective for deeper layers of ViT as learning to recover the residual of the masked image. We provide extensive empirical evidence showing that deeper ViTs can be effectively optimized using MIRL and easily gain accuracy from increased depth. With the same level of computational complexity as ViT-Base and ViT-Large, we instantiate 4.5$\times$ and 2$\times$ deeper ViTs, dubbed ViT-S-54 and ViT-B-48. The deeper ViT-S-54, costing 3$\times$ less than ViT-Large, achieves performance on par with ViT-Large. ViT-B-48 achieves 86.2% top-1 accuracy on ImageNet. On one hand, deeper ViTs pre-trained with MIRL exhibit excellent generalization capabilities on downstream tasks, such as object detection and semantic segmentation. On the other hand, MIRL demonstrates high pre-training efficiency. With less pre-training time, MIRL yields competitive performance compared to other approaches

No-cloning of nonorthogonal states does not require inner product preserving

The no-cloning theorem says there is no quantum copy machine which can copy any one-qubit state. Inner product preserving was always used to prove the no-cloning of nonorthogonal states. In this paper we show that the no-cloning of nonorthogonal states does not require inner product preserving and discuss the minimal properties which a linear operator possesses to copy two different states at the same device. In this paper, we obtain the following necessary and sufficient condition. For any two different states ∣ψ〉 = a∣0〉+b∣1〉∣ψ〉=a∣0〉+b∣1〉 and ∣ϕ〉 = c∣0〉+d∣1〉∣ϕ〉=c∣0〉+d∣1〉, assume that a linear operator LL can copy them, that is, L(∣ψ,0〉) = ∣ψ,ψ〉L(∣ψ,0〉)=∣ψ,ψ〉 and L(∣ϕ,0〉) = ∣ϕ,ϕ〉L(∣ϕ,0〉)=∣ϕ,ϕ〉. Then the two states are orthogonal if and only if L(∣0,0〉)L(∣0,0〉) and L(∣1,0〉)L(∣1,0〉) are unit length states. Thus we only need linearity and that L(∣0,0〉)L(∣0,0〉) and L(∣1,0〉)L(∣1,0〉) are unit length states to prove the no-cloning of nonorthogonal states. It implies that inner product preserving is not necessary for the no-cloning of nonorthogonal states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87751/2/082102_1.pd

Fixed-point Quantum Search for Different Phase Shifts

Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.Comment: 8 page

UNIDEAL: Curriculum Knowledge Distillation Federated Learning

Federated Learning (FL) has emerged as a promising approach to enable collaborative learning among multiple clients while preserving data privacy. However, cross-domain FL tasks, where clients possess data from different domains or distributions, remain a challenging problem due to the inherent heterogeneity. In this paper, we present UNIDEAL, a novel FL algorithm specifically designed to tackle the challenges of cross-domain scenarios and heterogeneous model architectures. The proposed method introduces Adjustable Teacher-Student Mutual Evaluation Curriculum Learning, which significantly enhances the effectiveness of knowledge distillation in FL settings. We conduct extensive experiments on various datasets, comparing UNIDEAL with state-of-the-art baselines. Our results demonstrate that UNIDEAL achieves superior performance in terms of both model accuracy and communication efficiency. Additionally, we provide a convergence analysis of the algorithm, showing a convergence rate of O(1/T) under non-convex conditions.Comment: Submitted to ICASSP 202

Task Indicating Transformer for Task-conditional Dense Predictions

The task-conditional model is a distinctive stream for efficient multi-task learning. Existing works encounter a critical limitation in learning task-agnostic and task-specific representations, primarily due to shortcomings in global context modeling arising from CNN-based architectures, as well as a deficiency in multi-scale feature interaction within the decoder. In this paper, we introduce a novel task-conditional framework called Task Indicating Transformer (TIT) to tackle this challenge. Our approach designs a Mix Task Adapter module within the transformer block, which incorporates a Task Indicating Matrix through matrix decomposition, thereby enhancing long-range dependency modeling and parameter-efficient feature adaptation by capturing intra- and inter-task features. Moreover, we propose a Task Gate Decoder module that harnesses a Task Indicating Vector and gating mechanism to facilitate adaptive multi-scale feature refinement guided by task embeddings. Experiments on two public multi-task dense prediction benchmarks, NYUD-v2 and PASCAL-Context, demonstrate that our approach surpasses state-of-the-art task-conditional methods.Comment: Accepted by ICASSP 202

The Simple Criteria of SLOCC Equivalence Classes

We put forward an alternative approach to the SLOCC classification of entanglement states of three-qubit and four-qubit systems. By directly solving matrix equations, we obtain the relations satisfied by the amplitudes of states. The relations are readily tested since in them only addition, subtraction and multiplication occur.Comment: The original version was submitted to PRA in Feb. 2005, the paper No. is AA10020. 14 pages for the present version. No figure