我们研究了连通图对应的图态中不同纠缠度的性质。结合图态的操作定义和纠缠测度的假设，证明了在N>3个量子比特的连通图态中不存在真正的三量子比特纠缠。对于某些类的图状态，所有真正的k量子比特纠缠，2 \leq k \leq N-1，在每k量子比特之间消失。这些关于连通图态的结果自然引出了完全多比特纠缠态的定义。我们还发现四量子比特的连通图态是一类但不是唯一的四量子比特完全纠缠态。
英文摘要：
We investigate the properties of different levels of entanglement in graph states which correspond to connected graphs. Combining the operational definition of graph states and the postulates of entanglement measures, we prove that in connected graph states of N>3 qubits there is no genuine three-qubit entanglement. For certain classes of graph states, all genuine k-qubit entanglement, 2\leq k\leq N-1, among every k qubits vanishes. These results about connected graph states naturally lead to the definition of fully multi-qubit entangled states. We also find that the connected graph states of four qubits is one but not the only one class of fully four-qubit entangled states.
Entangled graphs II: Classical correlations in multi-qubit entangled systems
多量子比特系统中的二分相关不能自由共享。某些量子位对上纠缠或经典相关的存在可能意味着其他量子位对上的相关。我们提出了一种方法，在多量子比特系统中使用纠缠图的概念，已经在我们的早期工作[M.Plesch和V.Buzek，Phys. Rev. A 67，012322（2003）]中引入的二分相关的特征。在纠缠图中，每个量子比特由一个顶点表示，而纠缠和经典关联由两种类型的边表示。通过构造证明了任何具有经典关联的纠缠图都可以用N个量子比特的混合态来表示。然而，并不是所有具有经典关联的纠缠图都可以用纯态来表示。
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error detection codes have been proposed and realized for lower number of qubit systems. Here we present an error detection code for a (2n+1)-qubit entangled state using two syndrome qubits and simulate it on IBM's 16-qubit quantum computer for a 13-qubit entangled system. The code is able to detect an arbitrary quantum error in any one of the first 2n qubits of the (…
We describe quantum circuits generating four-qubit maximally entangled states, the amount of entanglement being quantified by using the absolute value of the Cayley hyperdeterminant as an entanglement monotone. More precisely, we show that this type of four-qubit entangled states can be obtained by the action of a family of CNOT circuits on some special states of the LU orbit of the state |0000 >.
We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a "noisy" environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are "protected" against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglem…
We propose a new scheme in which perfect transmission of 1-qubit information is achieved with high success using purposefully delayed sharing of non-maximally entangled 2-qubit resource and repeated generalized Bell-state measurements (GBSM). Alice possesses initially all qubits and she makes repeated GBSM on the pair of qubits, consisting of (1) the qubit of information state and (2) one of the two entangled resource qubits (taken alternately) until transmission with perfect fidelity is indicated. Alice then sends to Bob, the qubit not used in the last GBSM and also the result of this GBSM an…
Analysis of Quantum Correlation in Successive Spin Measurements, Classical Communication of Spin $S$ Singlet States and Quantum Nonlocality of two Qubit Entangled States
Teleportation of Entangled States of a Vacuum-One Photon Qubit
我们报道了量子比特隐形传态的实验实现。量子比特在物理上是由电磁场模式的二维子空间实现的，具体地说，是由真空和单光子状态所跨越的空间。我们的实验遵循H. W. Lee和J.Kim，Phys.Rev.A，63，012305（2000）和E.Knill，R.Laflamme和G.Milburn Nature 409：46（2001）。
Recently, Ri-Gui Zhou et al. [Int. J. Theor. Phys. 59, 166-172 (2020)] proposed a scheme for bidirectional quantum teleportation of two-two and two-three qubit states by utilizing a six-qubit entangled state as a quantum channel. It is observed that the intrinsic efficiency calculated by Zhou et al. is not correct. In this improved scheme, we show that bidirectional teleportation of two-two and two-three qubit quantum states can be done by using optimized quantum resource and less consumption of classical resource. We also calculate the intrinsic efficiency of our improved scheme which is much…
Preparation of n-qubit Greenberger-Horne-Zeilinger entangled states in cavity QED: An approach with tolerance to nonidentical qubit-cavity coupling constants
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the walker's state from a classical to standard quantum-walk behavior, and a novel one. Additionally, we report on self-trapped behavior and perfect transfer with highest velocity for the walker. We also show that symmetry of probability density distribution, the most probable place to find the walker and evolution of the entropy are subject to initial entanglement bet…
We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories, when the qubits are measured. Depending on the measurement basis, these quantum trajectories can be jump-type or diffusive-type, and they can exhibit features not present with quantum optical and single-qubit trajectories. As an example, we consider the case of two remote atoms, where jump-type quantum trajectories herald the birth and death of entanglement.
We apply the support vector machine (SVM) algorithm to derive a set of entanglement witnesses (EW) to identify entanglement patterns in families of four-qubit states. The effectiveness of SVM for practical EW implementations stems from the coarse-grained description of families of equivalent entangled quantum states. The equivalence criteria in our work is based on the stochastic local operations and classical communication (SLOCC) classification and the description of the four-qubit entangled Werner states. We numerically verify that the SVM approach provides an effective tool to address the …
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
