We propose a deterministic scheme of generating genuine multiparty entangled states in quantum networks of arbitrary size having various geometric structures---we refer to it as entanglement circulation. The procedure involves optimization over a set of two-qubit arbitrary unitary operators and the entanglement of the initial resource state. We report that the set of unitary operators that maximize the genuine multipartite entanglement quantified via generalized geometric measure (GGM) is not unique. We prove that the GGM of the resulting state of arbitrary qubits coincides with the minimum GGM of the initial resource states. By fixing the output state as the six-qubit one, we find the optimal way to create such states according to the available resource. Moreover, we show that the method proposed here can be implemented by using logic gates, or by using the time dynamics of realizable spin Hamiltonians. In case of an ordered system, GGM varies periodically with time while the evolution via disordered models lead to a low but constant multipartite entanglement in outputs at a critical time, which decreases exponentially with the increase of the strength of the disorder.
Genuine multipartite entanglement (GME) is not only fundamentally interesting for the study of the quantum-to-classical transition, but also is essential for realizing universal quantum computing and quantum networks. Here, we investigate the multipartite entanglement (ME) dynamics in a linear chain of
NLC resonators interacting optomechanically with a common thermal acoustic reservoir. By presenting the exact analytical solutions of the system evolution, we predict the periodic generation of non-Gaussian ME, including discrete and continuous variable entanglement. Interestingly, GME is obtained even though the system is in a heat bath. The mechanism relies on a special acoustic environment featuring a frequency comb structure. More importantly, our proposed model also allows for the periodic generation of entangled multipartite cat states, i.e., a typical Greenberger-Horne-Zeilinger state, with high fidelity. This work fundamentally broadens the fields of ME, and has wide applications in implementing thermal-noise-resistant quantum information processing and many-body quantum simulation.
We investigate the emergence and properties of long-distance genuine multipartite entanglement, induced via three localized magnetic defects, in a one-dimensional transverse-field
XX spin-
1/2 chain. Using both analytical and numerical techniques, we determine the conditions for the existence of bound states localized at the defects. We find that the reduced density matrix (RDM) of the defects exhibits long-distance genuine multipartite entanglement (GME) across the whole range of the Hamiltonian parameter space, including regions where the two-qubit concurrence is zero. We quantify the entanglement by using numerical lower bounds for the GME concurrence, as well as by analytically deriving the GME concurrence in regions where the RDM is of rank 2. Our work provides insights into generating multipartite entanglement in many-body quantum systems via local control techniques.
We study
N qubits having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analytically solve the cases of
N=5 to 11 qubits, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities shows signatures of quantum integrability. For the general case of
N>11 qubits, we provide a conjecture on quantum integrability based on the numerical evidence such as degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics. Using linear entropy, we show that for the class of initial unentangled state, the entanglement periodically displays maximum and zero values.
Entanglement is a defining feature of many-body quantum systems and is an essential requirement for quantum computing. It is therefore useful to study physical processes which generate entanglement within a large system, as they maybe replicated for applications involving the said requirements in quantum information processing. A possible avenue to maximize entanglement generation is to rely on the phenomena of information scrambling, i.e. transport of initially localized information throughout the system. Here the rationale is that the spread of information carries with it an inherent capacity of entanglement generation. Scrambling greatly depends upon the dynamical nature of the system Hamiltonian, and the interplay between entanglement generation and information scrambling maybe investigated taking a chain of interacting spins on a one dimensional lattice. This system is analogous to an array of qubits and this relative simplicity implies that the resulting unitary dynamics can be efficiently simulated using present-day cloud based NISQ devices. In our present work, we consider such a spin model which is made up of nearest and next nearest neighbor XXZ Model, along with an introduced coupling term λ. This coupling term serves as a tuning parameter which modifies the dynamical nature of the system from the integrable to the quantum chaotic regime. In order to quantify the entanglement generated within the system we use the more general multipartite metric which computes the average entanglement across all system bipartitions to obtain a global picture of the entanglement structure within the entire system. Further to make our study initial state independent, we consider an ensemble of random initial states and evaluate the multipartite entanglement generated for each of these states under time evolution. We find clear differences in the entanglement measures as the system undergoes through different regimes. We also analyze the fluctuations present within our entanglement metric and find a distinct pattern as we head from the integrable to the chaotic regime.
Simple physical interactions between spin-
1∕2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin-
1∕2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin-
1∕2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter $\ensuremath{\lambda}$ has a maximum around the point $\ensuremath{\lambda}=1$, and it monotonically decreases for large values of $\ensuremath{\lambda}$. We prove that in the limit $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ this state is locally unitary equivalent to an
N-partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the
X-state). This
X-state exhibits the ``extreme'' entanglement in a sense that an arbitrary subset
A of $k\ensuremath{\leqslant}n$ qubits in the Ising chain composed of
N=2n+1 qubits is maximally entangled with the remaining qubits (set
B) in the chain. In addition, we prove that by performing a local operation just on the subset
B, one can transform the
X-state into a direct product of
k singlets shared by the parties
A and
B. This property of the
X-state can be utilized for new secure multipartite communication protocols.