We study translationally invariant rings of qubits with a finite number of sites N, and find the maximal nearest-neighbor entanglement for a fixed z component of the total spin. For small numbers of sites our results are analytical. The use of a linearized version of the concurrence allows us to relate the maximal concurrence to the ground state energy of an XXZ spin model, and to calculate it numerically for N<25. We point out some interesting finite-size effects. Finally, we generalize our results beyond nearest neighbors.
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 present a generalized criterion for maximally entangled nine-qubit states, whose minimum averaged subsystem purity should be equal to 1/14. In this note, we prove that absolutely maximally entangled state for nine qubits does not exist. Further, we construct a new genuine nine-qubit maximally entangled states of 110,15 and 1 balanced purities equal to 1/16, , 1/8 and and 1/4, respectively. We found that, the marginal density matrices for subsystems of 1,2,3- qubits all completely mixed in these states, therefore, maximally entangled nine-qubit state is a 3-uniform state.
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 investigate how arbitrary number of entangled qubits affects properties of quantum walk. We consider variance, positions with non-zero probability density and entropy as criteria to determine the optimal number of entangled qubits in quantum walk. We show that for a single walker in one-dimensional position space, walk with three entangled qubits show better efficiency in considered criteria comparing to the walks with other number of entangled qubits. We also confirm that increment in number of the entangled qubits results into significant drop in variance of probability density distributi…
We construct three-qubit entanglement witnesses with relatively simple structures. Despite their simplicity, these witnesses are capable of detecting a number of bound entangled states more effectively. To illustrate this, two families of bound entangled three-qubit states, introduced by Kay [Phys. Rev. A 83, 020303 (2011)] and Kye [J. Phys. A: Math. Theor. 48, 235303 (2015)], are considered and it is shown that these witnesses are able to detect the entanglement of all states in the families.
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。
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）。
Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trend…
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 the Markovian dynamics of a collection of n quantum systems coupled to an irreversible environmental channel consisting of a stream of n entangled qubits. Within the framework of repeated quantum interactions, we derive the master equation that describes the dynamics of the composite quantum system. We investigate the evolution of the joint system for two-qubit environments and find that (1) the presence of antidiagonal coherences (in the local basis) in the environment is a necessary condition for entangling two remote systems, and (2) that maximally entangled two-qubit baths are an …
We report on the coherence of Greenberger-Horne-Zeilinger (GHZ) states comprised of up to 8 qubits in the IBM ibmqx5 16-qubit quantum processor. In particular, we evaluate the coherence of GHZ states with $N=1,\ldots,8$ qubits, as a function of a delay time between state creation and measurement. We find that the decay in coherence occurs at a rate that is linear in the number of qubits. This is consistent with a model in which the dominant noise affecting the system is uncorrelated across qubits.
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 demonstrate one-sided device-independent self-testing of any pure entangled two-qubit state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable correlations, which certify all pure two-qubit entangled states. Our experimental results identify which particular pure two-qubit entangled state has been self-tested and which measurement operators are used on the untrusted side. Furthermore, we analytically derive the robustness bound of our protocol, enabling our subsequent experimental verification of …
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 …
