Witness for Non-Quasi Maximally Entangled States

Maximally entangled states, defined as those states that have the maximal entanglement of formation under some entanglement measure, are the ideal resource for many quantum missions. In this paper, we call a convex roof of maximally entangled pure states a quasi maximally entangled state. First, we present the concept of a witness for non-quasi maximally entangled states, which is an observable that can distinguish some non-quasi maximally entangled states from quasi maximally entangled ones. Then we prove that every non-quasi maximally entangled state can be witnessed by a witness and obtain some necessary and sufficient conditions for an observable to be a witness for non-quasi maximally entangled states. Lastly, we give some classes of Hermitian operators, which can become witnesses. Especially, we compute non-quasi maximally entangled states that can be detected by a specific product operator.     

Thermal entanglement versus mixture in a spin chain: Generation of maximally entangled mixed states

We study the two-body entanglement and mixture in a three-qubit XXZ spin chain in thermal equilibrium state at temperature T with an external magnetic field B. The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered. We show that the ground states in this system are fully characterized and distinguished by both entanglement and mixture. Thermal entanglement versus the mixture of all two-spin states is investigated. All pairwise states provide an upper bound on the entanglement for a fixed mixture, and some part of the boundary reaches the boundary allowed by physics. As a result, maximally entangled mixed states can be generated by controlling magnetic field and temperature. Especially, in the ground state of the whole system, the explicit forms of maximally entangled mixed states are given. The results provide a new way to generate maximally entangled mixed states and control entanglement.     

Quantum Entanglement of Many Distant Bose-Einstein Condensates in an Optical Lattice by Interference

We propose a scheme to generate maximally entangled states of two distant Bose-Einstein condensates, which are trapped in different potential wells of a one-dimensional optical lattice. We show how such maximally entangled state can be used to test the Bell inequality and realize quantum teleportation of a Bose-Einstein condensate state. The scheme proposed here is based on the interference of Bose-Einstein condensates leaking out from different potential wells of optical lattice. It is briefly pointed out that this scheme can be extended to generate maximally entangled Greenberger-Horne-Zeilinger (GHZ) states of 2m (m >1) distant Bose-Einstein condensates.     

Testing the nonlocality of entangled states by a new Bell-like inequality

We test a new four-qubit entangled state by the former Bell-like inequalities and find that it violates these inequalities, but not maximally. According to this entangled state, we build a new Bell-like inequality, which is violated by this new state maximally. We also determine the nonlocality of some other four-qubit states by the new inequality. It is found that the new inequality acts as a strong entanglement witness for the new state. This can be used to test new entangled states experimentally.     

Mixtures of maximally entangled pure states

We study the conditions when mixtures of maximally entangled pure states remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to ensure that the resulting mixed state is genuinely entangled. Also, we demonstrate how these results could be applied as a way to detect entanglement in mixtures of the entangled pure states with noise.     

Transformation of bipartite non-maximally entangled states into a tripartite W state in cavity QED

We present two schemes for transforming bipartite non-maximally entangled states into a W state in cavity QED system, by using highly detuned interactions and the resonant interactions between two-level atoms and a single-mode cavity field. A tri-atom W state can be generated by adjusting the interaction times between atoms and the cavity mode. These schemes demonstrate that two bipartite non-maximally entangled states can be merged into a maximally entangled W state. So the scheme can, in some sense, be regarded as an entanglement concentration process. The experimental feasibility of the schemes is also discussed.     

Nonmaximally entangled states can be better for multiple linear optical teleportation

We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via a nonmaximally entangled state, then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon: i.e., the total probability of successful multiple linear optical teleportation is higher for nonmaximally entangled states than maximally entangled states.     

三粒子纠缠Ｗ态的隐形传态

提出利用三个二粒子纠缠态作为量子信道，实现三粒子纠缠Ｗ态的隐形传态的方案.首先考察量子信道是最大纠缠态的情形，然后进一步考察量子信道是非最大纠缠态的情形.发现在量子信道为非最大纠缠态时，通过引进一个辅助粒子，并构造一个幺正变换矩阵，即可以一定的概率完成三粒子纠缠Ｗ态的隐形传态. 关键词： 隐形传态 三粒子纠缠 纠缠Ｗ态 非最大纠缠量子信道     

Scheme for realizing entanglement concentration via generalized measurements

How to concentrate non-maximally entangled states for quantum communication is a fundamental problem in quantum information. In this paper, we will apply generalized measurements to entanglement concentration of known non-maximally entangled pure states in arbitrary dimensional system. How to design the generalized measurements for the unambiguous discrimination of linearly independent non-orthogonal states is crucial for the concentration of the known non-maximally entangled states. The result shows that, any known non-maximally entangled pure state (for arbitrary dimensional system) can be transformed to the maximally entangled state only by introducing a qubit as ancilla and a joint unitary transformation operation on one of the entangled particles and the ancilla. In addition, because the less entangled state of each fail round will be re-concentrated too, the entanglement waste during the concentration process will be greatly reduced.     

Entanglement and Decoherence in Two-Dimensional Coherent State Superpositions

A detailed investigation of entanglement in the generalized two-dimensional nonorthogonal states, which are expressed in the framework of superposed coherent states, is presented. In addition to quantifying entanglement of the generalized two-dimensional coherent states superposition, necessary and sufficient conditions for maximality of entanglement of these states are found. We show that a large class of maximally entangled coherent states can be constructed, and hence, some new maximally entangled coherent states are explicitly manipulated. The investigation is extended to the mixed system states and entanglement properties of such mixed states are investigated. It is shown that in some cases maximally entangled mixed states can be detected. Furthermore, the effect of decoherence, due to both cavity losses and noisy channel process, on such entangled states are studied and its features are discussed.     

Optical parity gate and a wide range of entangled states generation

Generating entangled states efficiently is a hot topic in the area of quantum information science.With the approach presented in this paper,a general parity gate could be realized and a wide range of entangled states,including GHZ state,W state,Dicke state,arbitrary graph state and locally maximally entanglable states,can be generated flexibly.The generation of GHZ state,W state,and Dicke state is probabilistic but heralded and the total success probability is unit.In addition,the arbitrary graph state and locally maximally entanglable states generation is deterministic,flexible,and highly efficient.Especially,with the"simultaneous"generation pattern,the complexity of the graph state generation and locally maximally entanglable states generation could be reduced greatly,providing a more efficient and feasible way to generate the entangled states.     

Multipartite Fully Entangled Fraction

Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case, we call the generalized version multipartite fully entangled fraction (MFEF). MFEF measures the closeness of a state to GHZ states. The analytical expressions of MFEF are very difficult to obtain except for very special states, however, we show that, the MFEF of any state is determined by a system of finite-order polynomial equations. Therefore, the MFEF can be efficiently numerically computed.     

Generation of multipartite entangled states by cavity QED

We propose the methods of generating multipartite entanglement by considering the interaction of a system of N two-level atoms in M cavities of high quality factor with a strong classical driving field. It is shown that, with the cavity detuning, the applied driving field detuning and vacuum Rabi coupling, we can produce an entangled coherent state in two single-mode cavities and generate the entangled coherent cluster states in two bimodal vacuum cavities. Tuning these parameters also allows us to acquire the anti-Jaynes-Cummings （AJC） interaction, with which we can generate the maximally two-photon entangled states, and the two-atom and the two-photon entangled cluster states.     

Experimental realization of deterministic entanglement transformations of bipartite pure states

We experimentally realize a kind of entanglement transformations of bipartite pure states with 100% efficiency. The protocol employs two-outcome positive operator-valued measures (POVMs) and can transform two-photon maximally entangled state to any two-photon entangled pure state with 100% efficiency. The average fidelity of all output states is 96%. Moreover, the scheme to implement arbitrary POVM on single-photon polarization state is also discussed. In principle, our setup can be applied to any kind of entanglement transformations of two-qubit entangled states to achieve optimal successful probability.     

Cooperative Communications via Dual-Teleportation with Non-maximally Entanglement Measurements

We investigate a framework of the cooperative quantum teleportation (CQT) based on non-maximally entangled state basis (NB) measurements, instead of maximally entangled state basis (MB) measurements. It is implemented with two consecutive conventional (or direct) quantum telportations (DQT), where unknown quantum states can be transmitted in a point-to-point fashion. The security is based on the quantum-mechanical impossibility of local unitary transformations between non-maximally entangled states. It shows that the CQT can enhance the successful transmissions by self-correcting the errors introduced in the dual-teleportations.     

Preparation of Multi—Atom Entangled States with a Single Cavity in a Thermal State

A scheme is suggested for the generation of multi-atom maximally entangled states with a cavity in a thermal state,In this scheme several appropriately prepared two-level atoms are simultaneously sent through the nonresonant cavity.We divide the whole atom-cavity interaction time into two equal parts.At the end of the first part a π pulse is applied to the atome using a classical field.Then the photon-number-dependent shifts on the atomic states are cancelled and the atomic system finally evoloves to a maximally entangled state.     

Quantum gates and multiparticle entanglement by Rydberg excitation blockade and adiabatic passage

We propose to apply stimulated adiabatic passage to transfer atoms from their ground state into Rydberg excited states. Atoms a few micrometers apart experience a dipole-dipole interaction among Rydberg states that is strong enough to shift the atomic resonance and inhibit excitation of more than a single atom. We show that the adiabatic passage in the presence of this interaction between two atoms leads to robust creation of maximally entangled states and to two-bit quantum gates. For many atoms, the excitation blockade leads to an effective implementation of collective-spin and Jaynes-Cummings-like Hamiltonians, and we show that the adiabatic passage can be used to generate collective J_{x}=0 eigenstates and Greenberger-Horne-Zeilinger states of tens of atoms.     

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.     

Scheme for purifying a general mixed entangled state and its linear optical implementation

We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.     

From Quantum State Targeting to Bell Inequalities

Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally entangled states. The optimal solution of the game is used to derive a Bell inequality for two entangled qutrits. We argue that the nice properties of the inequality are direct consequences of the method of construction.