Upper bound on singlet fraction of two-qubit mixed entangled states

We demonstrate a new method to achieve the maximum singlet fraction using an entangled mixed two-qubit state as a resource. For this, we establish a tight upper bound on singlet fraction and show that the maximal singlet fraction obtained in Verstraete and Verschelde (Phys Rev Lett 90:097901(1)–097901(4), 2003) does not attain the upper bound on the singlet fraction derived here. Interestingly, we found that the required upper bound can, in fact, be achieved using local filtering operations.     

Geometric discord and measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ( $2\otimes 4, 3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett et al.’s in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti et al. and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.     

基于高维纠缠态的量子密钥分发协议

为了提高量子密钥分发的效率和安全性,利用高维Hilbert空间中的Bell态和Hadamard门设计了一种量子密钥分发协议。首先通过量子态的动态演变验证了三维Bell纠缠态在Z基和X基下具有不同的表示特性,然后以此为基础进行协议设计,其中利用Z基测量来检测窃听,利用X基测量来产生密钥。安全性分析表明,该协议可以抵抗截获重发、纠缠附加粒子和特洛伊木马三种常见的攻击。最后将协议与其他方案进行了比较,该协议在保证量子比特效率50%的基础上,安全性也有所提升。     

基于纠缠的量子密钥分配协议仿真

由于受物理资源和实验条件的限制,在经典计算机上对量子密钥分配（QKD）仿真,为研究者提供一种手段以便更好地掌握这类抽象协议。对以纠缠态为基础的E91协议的量子密钥分配过程进行仿真,重点对比分析了理想环境、有噪环境以及窃听环境下的仿真结果,并验证该量子密钥分配协议的安全性。     

Two authenticated quantum dialogue protocols based on three-particle entangled states

In this paper, we propose two authenticated quantum dialogue protocols based on three-particle entangled states, which are both completely secure and more efficient. The first controlled quantum dialogue protocol with authentication is creatively proposed, which is secure under not only some famous external attacks but also internal attacks, for example, the dishonest controller’s attack. This protocol has a slightly increasing efficiency and less qubit cost compared to previous protocols. Besides, we present the second authenticated quantum dialogue protocol, which has a high efficiency with 80% by integrating dense coding. This protocol can also resist various well-known attacks.     

A lower bound for sorting networks based on the shuffle permutation

We prove an (lg² n/lg lgn) lower bound for the depth ofn-input sorting networks based on the shuffle permutation. The best previously known lower bound was the trivial (lgn) bound, while the best upper bound is given by Batcher's (lg² n)-depth bitonic sorting network. The proof technique employed in the lower bound argument may be of independent interest.C. G. Plaxton was supported by NSF Research Initiation Award CCR-9111591, and the Texas Advanced Research Program under Grant No. 003658-480. T. Suel was supported by the Texas Advanced Research Program under Grant No. 003658-480, and by an MCD Fellowship of the University of Texas at Austin.     

两个基于四粒子纠缠态的量子秘密共享方案

本文分别基于四粒子Cluster态和一个非对称的四粒子纠缠态,提出两个量子秘密共享的方案,其中共享的秘密是未知的单粒子态。秘密的发送者需要对手中的粒子进行Bell基测量,协助者需要对手中的粒子进行测量或者实施幺正操作,最后接收者通过对手中的粒子进行相应的幺正变换或者受控非门操作,就可以重构原始秘密。通过分析表明,任何一个代理者在其他两方协助下是可以恢复秘密的,所以我所提出的方案是高效且安全可靠的。     

A lower bound on the area of permutation layouts

In this paper we prove a tight Ω(n ³) lower bound on the area of rectilinear grids which allow a permutation layout ofn inputs andn outputs. Previously, the best lower bound for the area of permutation layouts with arbitrary placement of the inputs and outputs was Ω(n ²), though Cutler and Shiloach [CS] proved an Ω(n ^2.5) lower bound for permutation layouts in which the set of inputs and the set of outputs each lie on horizontal lines. Our lower bound also holds for permutation layouts in multilayer grids as long as a fixed fraction of the paths do not change layers.     

A lower bound on the area of permutation layouts

In this paper we prove a tight (n ³) lower bound on the area of rectilinear grids which allow a permutation layout ofn inputs andn outputs. Previously, the best lower bound for the area of permutation layouts with arbitrary placement of the inputs and outputs was (n ²), though Cutler and Shiloach [CS] proved an (n ^2.5) lower bound for permutation layouts in which the set of inputs and the set of outputs each lie on horizontal lines. Our lower bound also holds for permutation layouts in multilayer grids as long as a fixed fraction of the paths do not change layers.The first author's research was partially supported by NSF Grant No. MCS 820-5167. The third author's research was supported by NSF Grant No. MCS-8204246 and by a Hebrew University Fellowship.     

Local cloning of multipartite entangled states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.     

Preparing entangled states by Lyapunov control

By Lyapunov control, we present a protocol to prepare entangled states such as Bell states in the context of cavity QED system. The advantage of our method is of threefold. Firstly, we can only control the phase of classical fields to complete the preparation process. Secondly, the evolution time is sharply shortened when compared to adiabatic control. Thirdly, the final state is steady after removing control fields. The influence of decoherence caused by the atomic spontaneous emission and the cavity decay is discussed. The numerical results show that the control scheme is immune to decoherence, especially for the atomic spontaneous emission from \(|2\rangle \) to \(|1\rangle \). This can be understood as the state staying in an invariant subspace. Finally, we generalize this method in preparation of W state.     

Creating maximally entangled states by gluing

We introduce a general method of gluing multi-partite states and show that entanglement swapping is a special class of a wider range of gluing operations. The gluing operation of two m and n qudit states consists of an entangling operation on two given qudits of the two states followed by operations of measurements of the two qudits in the computational basis. Depending on how many qudits (two, one or zero) we measure, we have three classes of gluing operation, resulting respectively in \(m+n-2\), \(m+n-1\), or \(m+n\) qudit states. Entanglement swapping belongs to the first class and has been widely studied, while the other two classes are presented and studied here. In particular, we study how larger GHZ and W states can be constructed when we glue the smaller GHZ and W states by the second method. Finally we prove that when we glue two states by the third method, the k-uniformity of the states is preserved. That is when a k-uniform state of m qudits is glued to a \(k'\)-uniform state of n qudits, the resulting state will be a \(\hbox {min}(k,k')\)-uniform of \(m+n\) qudits.     

Telecloning of qudits via partially entangled states

Quantum Information Processing - We study the process of quantum telecloning of d-dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently...     

One-way LOCC indistinguishability of maximally entangled states

In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of $d-1$ indistinguishable maximally entangled states by one-way LOCC are demonstrated in $d \otimes d$ (for $d=7, 8, 9, 10$ ). Interestingly, we discover there exist sets of $d-2$ such states in $d \otimes d$ (for $d=8, 9, 10$ ), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist $d-1$ or fewer indistinguishable maximally entangled states in $d \otimes d(d \ge 5)$ by one-way LOCC.     

Multi-mode entangled states represented as Grassmannian polynomials

Quantum Information Processing - We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map...     

Optimal remote preparation of arbitrary multi-qubit real-parameter states via two-qubit entangled states

In this paper, we present an efficient scheme for remote state preparation of arbitrary n-qubit states with real coefficients. Quantum channel is composed of n maximally two-qubit entangled states, and several appropriate mutually orthogonal bases including the real parameters of prepared states are delicately constructed without the introduction of auxiliary particles. It is noted that the successful probability is 100% by using our proposal under the condition that the parameters of prepared states are all real. Compared to general states, the probability of our protocol is improved at the cost of the information reduction in the transmitted state.     

任意二粒子纠缠态的受控量子通信

为了解决任意二量子通信问题,首先给出了五粒子和七粒子纠缠态的构造方法,并提供了它们的量子线路图。其次,以该五粒子纠缠态为量子信道,提出一个任意二粒子未知量子态的受控隐形传态协议。该协议在监察者Charlie的控制下,Alice进行四粒子投影测量和经典通信,Bob采用简单酉变换就能以100%的概率成功重构一个任意二粒子纠缠态。最后,利用七粒子纠缠态为量子信道,提出了任意二粒子纠缠态的联合受控远程制备方案。在此方案中,发送者Alice用自己掌握被制备态的部分信息构造测量基,发送者Bob采用前馈测量策略,接收者Diana在监控者Charlie的帮助下,通过简单幺正变换就能确定性地恢复原始态。     

Deterministic remote preparation of arbitrary multi-qubit equatorial states via two-qubit entangled states

We propose an efficient scheme for remotely preparing an arbitrary n-qubit equatorial state via n two-qubit maximally entangled states. Compared to the former scheme (Wei et al. in Quantum Inf Process 16:260, 2017) that has the 50% successful probability when the amplitude factors of prepared states are \(2^{-n{/}2}\), the probability would be increased to 100% by using of our modified proposal. The feasibility of our scheme for remote preparation arbitrary multi-qubit equatorial states is explicitly demonstrated by theoretical studies and concrete examples.