Extremal properties of conditional entropy and quantum discord for XXZ,symmetric quantum states

For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy \(S_{cond}\) as a function of measurement angle \(\theta \in [0,\pi /2]\). Numerical calculations show that the function \(S_{cond}(\theta )\) for X states can have at most one local extremum in the open interval from zero to \(\pi /2\) (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle \(\theta ^*\). Such \(\theta \)-regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval \((0,\pi /2)\). It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.     

Quantum teleportation through noisy channels with multi-qubit GHZ states

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for \(n\) -qubit GHZ states \(n\in \{4,5,6\}\) where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than \(n\) GHZ state under most noisy channels. However, \(n\) GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in \(x\) direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.     

Fault tolerant deterministic quantum communications using GHZ states over collective-noise channels

This study proposes two new coding functions for a GHZ state and a GHZ-like state, respectively. Based on these coding functions, two fault tolerant deterministic quantum communication (DQC) protocols are proposed. Each of the new DQC’s is robust under one kind of collective noises: collective-dephasing noise and collective-rotation noise, respectively. The sender can use the proposed coding functions to encode his/her message, and the receiver can perform the Bell measurement to obtain the sender’s message. In comparison to the existing fault tolerant DQC protocols over collective-noise channels, the proposed protocols provide the best qubit efficiency. Moreover, the proposed protocols are also free from the ordinary eavesdropping and the information leakage.     

Fault tolerant quantum key distributions using entanglement swapping of GHZ states over collective-noise channels

This work proposes two fault tolerant quantum key distribution (QKD) protocols. Each of which is robust under one kind of collective noises: collective-dephasing noise and collective-rotation noise, respectively. Due to the use of the entanglement swapping of Greenberger–Horne–Zeilinger (GHZ) state as well as the decoy logical qubits, the new protocols provide the best qubit efficiency among the existing fault tolerant QKD protocols over the same collective-noise channel. The receiver simply performs two Bell measurements to obtain the raw key. Moreover, the proposed protocols are free from several well-known attacks and can also be secure over a lossy channel.     

Ordering states with Tsallis relative $$\alpha $$-entropies of coherence

In this paper, we study the ordering states with Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative \(\alpha \)-entropies of coherence and \(l_{1}\) norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative \(\alpha \)-entropies of coherence for \(\alpha =2, 1, \frac{1}{2}\) and show these three measures and \(l_{1}\) norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between \(l_{1}\) norm of coherence and Tsallis relative \(\alpha \)-entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.     

Comparison of quantum discord and relative entropy in some bipartite quantum systems

The study of quantum correlations in high-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical–classical state. In particular, we establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit–qutrit have been demonstrated.     

Study of quantum correlation swapping with relative entropy methods

To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs (Xie et al. in Quantum Inf Process 14:653–679, 2015). In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method (Modi et al. in Phys Rev Lett 104:080501, 2010), the Zhang method (arXiv:1011.4333 [quant-ph]) and the RS method (Rulli and Sarandy in Phys Rev A 84:042109, 2011). We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.     

Superactivation of quantum channels is limited by the quantum relative entropy function

In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical connection between the quantum relative entropy function and the superactivation effect was completely unrevealed. We demonstrate the results for the quantum capacity; however the proposed theorems and connections hold for all other channel capacities of quantum channels for which the superactivation is possible.     

基于GHZ态的无酉操作多方量子秘密共享方案

为了简化多方量子秘密共享协议,利用Greenberger-Horne-Zeilinger（GHZ）态和互补基特性,提出了一种简单高效的多方量子秘密共享方案。该方案无需进行任何酉操作,发送方和多个接收方之间只需一次量子通信,并使用互补基进行测量即可完成信道安全检测和秘密共享。除去少量用于检测量子信道安全的粒子,其余每个GHZ态粒子共享一个比特的经典信息。安全性分析表明该方案是安全可靠的。     

Generating multi-mode entangled coherent W and GHZ states via optical system based fusion mechanism

Fusion technology has been demonstrated to be a good method for generating a large-scale entangled coherent W or GHZ state from two small ones in QED system. It is of importance to study how to fuse small-scale entangled coherent W or GHZ states via optical system. In this paper, we present a scheme for generating larger entangled coherent W or GHZ state in an optical system by virtue of fusion technology. The key fusion mechanism is realized by photon detectors and a Mach–Zehnder interferometer with its two arms immersed in Kerr media, by which an n-mode entangled coherent W state and an m-mode entangled coherent W state can be probabilistically fused into an (\(n+m-2\))-mode entangled coherent W state. This fusion scheme applies to entangled coherent GHZ state too but with a unit probability of success. Feasibility analysis indicates that our fusion scheme may be realized with current experimental technology. Large-scale entangled coherent W and GHZ states may find new applications in quantum communication.     

The quantum relative entropy as a rate function and information criteria

We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are essentially based on Hiai-Ohya-Tsukada theorem.

     

利用混沌PSO或分解的2维Tsallis灰度熵阈值分割

现有最大Shannon熵或Tsallis熵阈值选取方法没有从类内灰度均匀性出发,而仅依据图像灰度直方图,并且Tsallis熵法的分割效果通常优于Shannon熵法。为此,提出了基于混沌粒子群优化(PSO)和基于分解的两种2维Tsallis灰度熵阈值分割方法。首先,给出了1维Tsallis灰度熵阈值选取方法并将其推广到2维,导出了相应的2维Tsallis灰度熵阈值选取公式及其递推算法;其次,利用混沌PSO算法搜寻2维Tsallis灰度熵法的最佳阈值,并采用递推方式去除迭代过程中适应度函数的冗余运算,大大提高了运行速度;最后,将2维Tsallis灰度熵阈值选取方法的运算转化为两个1维Tsallis灰度熵法的运算,计算复杂度从O(L2)进一步降低到O(L)。实验结果表明,与2维最大Shannon熵法、2维最大Tsallis熵法及2维Tsallis交叉熵法相比,所提出的两种方法可以大幅提高图像分割质量和算法运行速度。     

Bidirectional teleportation of a pure EPR state by using GHZ states

In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on controlled-not operation, single-qubit measurement, and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other, While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous protocols.     

Multi-level thresholding based on differential evolution and Tsallis Fuzzy entropy

This paper presents a multilevel image thresholding approach which relies on Tsallis entropy using Fuzzy partition with a novel threshold selection technique. In order to compute the optimal threshold values, Differential Evolution (DE) has been employed. The proposed method can further be exploited in image segmentation which is considered to be a critical step in image processing. Our proposed threshold selection technique is based on Tsallis-Fuzzy entropy and the results are compared with Shannon entropy (or fuzzy entropy) and Tsallis entropy based existing threshold selection techniques. The experiments are performed on two different sets of images and the results have been compared with that of existing state-of-the-art methods, namely, Patch Levy Bees' Algorithm (PLBA), Bacterial Foraging optimization (BFO), modified Bacterial Foraging optimization (MBFO) and Bees' Algorithm (BA). Quantitative analysis is carried out based on three image quality metrics viz SSIM, PSNR and SNR. Standard deviation and CPU time for convergence of the objective function have been calculated for performance evaluation. Furthermore, the statistical significance of our method has been estimated using Friedman test and Wilcoxon test. The experimental results manifest that our method produces results superior to the methods in comparison.     

Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states

A method for calculating the one-way quantum deficit is developed. It involves a careful study of post-measured entropy shapes. We discovered that in some regions of X-state space the post-measured entropy \(\tilde{S}\) as a function of measurement angle \(\theta \in [0,\pi /2]\) exhibits a bimodal behavior inside the open interval \((0,\pi /2)\), i.e., it has two interior extrema: one minimum and one maximum. Furthermore, cases are found when the interior minimum of such a bimodal function \(\tilde{S}(\theta )\) is less than that one at the endpoint \(\theta =0\) or \(\pi /2\). This leads to the formation of a boundary between the phases of one-way quantum deficit via finite jumps of optimal measured angle from the endpoint to the interior minimum. Phase diagram is built up for a two-parameter family of X states. The subregions with variable optimal measured angle are around 1\(\%\) of the total region, with their relative linear sizes achieving \(17.5\%\), and the fidelity between the states of those subregions can be reduced to \(F=0.968\). In addition, a correction to the one-way deficit due to the interior minimum can achieve \(2.3\%\). Such conditions are favorable to detect the subregions with variable optimal measured angle of one-way quantum deficit in an experiment.     

Generation of GHZ states with invariant-based shortcuts

A scheme is proposed to generate three-atom GHZ states by applying the inversely engineered control method on the basis of Lewis–Riesenfeld invariants. In the proposal, three atoms that have different configurations are trapped in a bimodal cavity. Numerical simulations indicate that our protocol has an obvious improvement of speed for the generation of GHZ states. Moreover, the present scheme is robust against both parameter fluctuations and dissipation.     

Optimum anamorphic image generation using image rotation and relative entropy

Multimedia Tools and Applications - Anamorphosis is related to the art that gives illusion (distortion) over the image or object when the viewer looks the original image or from the random...     

基于引导滤波和Tsallis熵的SAR图像分割算法

针对合成孔径雷达(SAR)图像易受噪声干扰、分割方法精度低的问题,提出了一种基于频域引导滤波和Tsallis熵的SAR图像多阈值分割算法.利用非下采样Contourlet变换(NSCT)对图像多尺度分解,提取图像各方向的高频信息;通过引导滤波增强高频分量的边缘信息,在保持边缘的同时抑制了相干斑噪声;利用改进的二维Tsallis熵多阈值对增强图像精确分割.实验结果表明:分割算法对噪声不敏感,分割精度和适应性明显提高.     

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Program summaryProgram title: TRQSCatalogue identifier: AEKA_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7924No. of bytes in distributed program, including test data, etc.: 88 651Distribution format: tar.gzProgramming language: Mathematica, CComputer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of MathematicaOperating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit)RAM: Case dependentClassification: 4.15Nature of problem: Generation of random density matrices.Solution method: Use of a physical quantum random number generator.Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.     

Extension of Yager's negation of a probability distribution based on Tsallis entropy

The negation of probability distribution becomes an important topic since some problems are burdensome to deal with directly. Inspired by Yager's negation of probability distribution, an extension model to measure the negation of a probability distribution is proposed using the idea of a nonextensive statistic based on Tsallis entropy. Proofs show that the proposed extension of negation of probability distribution converges to the maximum Tsallis entropy. The proposed model may extend Yager's method to consider the influences of the correlations in a system, which gives the different convergent routes. Some numerical simulation results are used to illustrate the effectiveness of the proposed methodology.