Genuine Entanglement Research Articles

Generation of Massive Entanglement through an Adiabatic Quantum Phase Transition in a Spinor Condensate

We propose a method to generate massive entanglement in a spinor Bose-Einstein condensate from an initial product state through an adiabatic sweep of the magnetic field across a quantum phase transition induced by competition between the spin-dependent collision interaction and the quadratic Zeeman effect. The generated many-body entanglement is characterized by the experimentally measurable entanglement depth in the proximity of the Dicke state. We show that the scheme is robust to practical noise and experimental imperfection and under realistic conditions it is possible to generate genuine entanglement for hundreds of atoms.

Proof of the Gour-Wallach conjecture

The absolute value of the hyperdeterminant of four qubits is a useful measure of genuine entanglement. We prove a recent conjecture of Gour and Wallach describing the pure maximally entangled four-qubit states with respect to this measure.

Entanglement criteria for Dicke states

Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and they have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the vicinity of these states. We use the approach of positive partial transpose mixtures to derive the conditions analytically. For nearly all cases, our criteria are stronger than all conditions previously known.

Genuine quadripartite macroscopic entanglement generated in two-mode optomechanical systems

We propose a scheme to generate stationary quadripartite entanglement in two-mode optical Fabry-Perot cavity, which consisted of the same two fixed mirrors and the same two perfectly reflective movable mirrors. We treat the whole two-cavity fields-two movable mirrors system as intrinsically quadripartite and investigate quadripartite continuous-variable (CV) entanglement among them. Using the criterion proposed by Loock and Furrsawa, we demonstrate that genuine quadripartite CV entanglement can be generated in this system. This system will provide a way to create genuine quadripartite entanglement in a macroscopic level and will hold good prospects for quantum information and quantum networks.

Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices

We consider a class of large superposed states, obtained from dimer coverings on spin-1/2 isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty entangled, irrespective of the geometry and dimension of the isotropic lattice. We then present an efficient method to characterize the genuine multisite entanglement in the case of isotropic square spin-1/2 lattices, with short-range dimer coverings. We use this iterative analytical method to calculate the multisite entanglement of finite-sized lattices, which through finite-size scaling, enables us to obtain the estimate of the multisite entanglement of the infinite square lattice. The method can be a useful tool to investigate other single- and multisite properties of such states.

Experimental preparation and nonlocality of the high-pure four-photon Greenberger-Horne-Zeilinger states

Using the spontaneous parametric down conversion and post-selection method, we experimentally prepare the four-photon Greenberger-Horne-Zeilinger (GHZ) states with a high fidelity about 83.1%. Then, an efficiently method to improve the contrast ratio of the four-photon state is reported by theoretical analysis and experiment optimization. Based on the state, we study the local realism of this state and achieve 28 standard deviations, confirm the existence of genuine four-particle entanglement. Our work has important significance for experimental preparation and studying nonlocality of the high-fidelity multiple-photon entanglement states.

Genuine multiparticle entanglement of permutationally invariant states

We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of positive partial transpose mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.

Intermodal entanglement in Raman processes

The operator solution of a completely quantum mechanical Hamiltonian of the Raman processes is used here to investigate the possibility of obtaining intermodal entanglement between different modes involved in the Raman processes [e.g., pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode]. Intermodal entanglement is reported between (a) pump mode and anti-Stokes mode, (b) pump mode and vibration (phonon) mode, (c) Stokes mode and vibration phonon mode, and (d) Stokes mode and anti-Stokes mode in the stimulated Raman processes for variation of the phase angle of complex eigenvalue ${\ensuremath{\alpha}}_{1}$ of pump mode $a$. Some incidents of intermodal entanglement in the spontaneous and the partially spontaneous Raman processes are also reported. Further, it is shown that the specific choice of coupling constants may produce genuine entanglement among Stokes mode, anti-Stokes mode, and vibration-phonon mode. It is also shown that the two-mode entanglement not identified by Duan's criterion may be identified by Hillery-Zubairy criteria. It is further shown that intermodal entanglement, intermodal antibunching, and intermodal squeezing are independent phenomena.

Genuine entanglement of four-qubit cluster diagonal states

We reduce the necessary and sufficient biseparable conditions of the four qubit cluster diagonal state to concise forms. Only 4 out of the 15 parameters are proved to be relevant in specifying the genuine entanglement of the state. Using the relative entropy of entanglement as the entanglement measure, we analytically find the genuine entanglement of all the four qubit cluster diagonal states. The formulas of the genuine entanglement are of five kinds, for seven different parameter regions of entanglement.

Identification of three-qubit entanglement

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.

Genuine entanglement among coherent excitonic states of three quantum dots located individually in separated coupled QED cavities

New scheme for generating genuine three-partite entanglement among three quantum dots (QDs) is proposed. The QDs are trapped in an one-dimensional (1D) array of three equidistance single-mode coupled cavities. Photon hopping is considered to be responsible for coupling between the cavities. The effective dynamics of the system leads to generate genuine three-partite entangled coherent excitonic states in QDs. The entanglement of these states, after encoding as three-qubit system, can be detected by entanglement witnesses (EWs) based on GHZ-states. It is shown that the generated entangled states can be arbitrarily very close to the GHZ-states.

The density matrix recursion method: genuine multisite entanglement distinguishes odd from even quantum spin ladder states

We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size for the even-legged ladder states, it does the opposite for odd-legged ones.

Relating monogamy of quantum correlations and multisite entanglement

There are two important paradigms for defining quantum correlations in quantum information theory, viz. the information-theoretic and the entanglement-separability ones. We find an analytical relation between two measures of quantum correlations, one in each paradigm, and show that only a certain cone-like region on the two-dimensional space spanned by these measures is accessible to pure three-qubit states. The information-theoretic multiparty quantum correlation measure is related to the monogamy considerations of a bipartite information-theoretic quantum correlation measure, while the entanglement-separability multiparty measure is the generalized geometric measure, a genuine multiparty entanglement measure. We also find an analytical relation between two multiparty entanglement measures, and again obtain a cone-like accessible region in this case. One of the multisite measures in this case is related to the monogamy of a bipartite entanglement measure, while the other is again the generalized geometric measure. Just like in relativity, events cannot occur outside the space-time light cone, we analogously find here that state points corresponding to pure three-qubit states cannot fall outside the two-dimensional cone-like structure between quantum monogamy scores and a genuine multisite entanglement measure.

Observation of the Emergence of Multipartite Entanglement Between a Bipartite System and its Environment

The dynamics of the environment is usually experimentally inaccessible and hence ignored for open systems. Here we overcome this limitation by using an interferometric setup that allows the implementation of several decoherence channels and full access to all environmental degrees of freedom. We show that when a qubit from an entangled pair interacts with the environment, the initial bipartite entanglement gets redistributed into bipartite and genuine multipartite entanglements involving the two qubits and the environment. This is yet another trait of the subtle behavior of entangled open systems.

Defeating entanglement sudden death by a single local filtering

Genuine multipartite entanglement of a quantum system can be partially destroyed by local decoherence. Is it possible to retrieve the entanglement to some extent by a single local operation? The answer to this question depends very much on the type of initial genuine entanglement. For initially pure W and cluster states and if the decoherence is given by generalized amplitude damping, the answer is shown to be positive. In this case, the entanglement retrieving is achieved just by redistributing the remained entanglement of the system.

Three-particle entanglement swapping in an imperfect channel

Extending our previous work [J. Korean Phys. Soc. 58, 1708 (2011)], we analyze the noise effects of an imperfect channel on three-particle entanglement swapping by calculating the fidelity F of a three-qubit state after a GHZ measurement. In contrast to other kinds of noise, the bit flip noise and the phase flip noise do not cause the fidelity to decay exponentially to 0.25 but to 0.5, which shows the presence of genuine entanglement.

Markovianity criteria for quantum evolution

We characterize a class of Markovian dynamics using the concept of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a simple observation that Markovian dynamics implies monotonic behaviour of several well-known quantities such as distinguishability of states, fidelity, relative entropy and genuine entanglement measures.

Package of facts and theorems for efficiently generating entanglement criteria for many qubits

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine 5-qubit entanglement without ever referring to correlations between all five qubits.

Discrete Fourier-Based Correlations for Entanglement Detection

We introduce two forms of correlations on two d-level (qudit) systems for entanglement detection. The correlations can be measured via experimentally tractable two local measurement settings and their separable bounds are determined by discrete Fourier-based uncertainty relations. They are useful to estimate lower bounds of the Schmidt number in order to clarify generation of a genuine qudit entanglement. We also present inseparable conditions for multiqudit systems associated with the qudit stabilizer formalism as another role of the correlations on the inseparability problem.

Experimental realization of a four-photon seven-qubit graph state for one-way quantum computation

We propose and demonstrate the scaling up of photonic graph states through path qubit fusion. Two path qubits from separate two-photon four-qubit states are fused to generate a two-dimensional seven-qubit graph state composed of polarization and path qubits. Genuine seven-qubit entanglement is verified by evaluating the witness operator. Six qubits from the graph state are used to demonstrate the Deutsch-Jozsa algorithm for general two-bit functions with a success probability greater than 90%.