Topological entanglement in Abelian and non-Abelian excitation eigenstates

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the excitations of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.     

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.     

Entanglement of a two-particle Gaussian state interacting with a heat bath

The effect of a thermal reservoir is investigated on a bipartite Gaussian state. We derive a pre-Lindblad master equation in the non-rotating wave approximation for the system. We then solve the master equation for a bipartite harmonic oscillator Hamiltonian with entangled initial state. We show that for strong damping the loss of entanglement is the same as for freely evolving particles. However, if the damping is small, the entanglement is shown to oscillate and eventually tend to a constant non-zero value.     

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.     

Aspects of Entanglement in Quantum Many-Body Systems

Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions.     

Anti-symmetry consideration on the preservation of entanglement of spin system

In this work we offer an approach to protect the entanglement based on the anti-symmetric property of the Hamiltonian. Our main objective is to protect the entanglement of a given initial three-qubit state which is governed by Hamiltonian of a three-spin Ising chain in site-dependent transverse fields. We show that according to anti-symmetric property of the Hamiltonian with respect to some operators mimicking the time reversal operator, the dynamics of the system can be effectively reversed. It equips us to control the dynamics of the system. The control procedure is implemented as a sequence of cyclic evolution; accordingly the entanglement of the system is protected for any given initial state with any desired accuracy and long-time. Using this approach we could control not only the multiparty entanglement but also the pairwise entanglement. It is also notable that in this paper although we restrict ourselves mostly within a three-spin Ising chain in site-dependent transverse fields, our approach could be applicable to any n$n$-qubit spin system models.     

Adiabatic switching approach to multidimensional supersymmetric quantum mechanics for several excited states

We present a time-dependent method for determining several approximate excited-state energies and wave functions using a vectorial approach to multidimensional supersymmetric quantum mechanics. First, a vectorial approach is used to generate the tensor sector two Hamiltonian, which is isospectral with the original scalar sector one Hamiltonian above the ground state of the sector one Hamiltonian. We construct a time-dependent Hamiltonian interpolating between the scalar sector one Hamiltonian and the tensor sector two Hamiltonian. Then, we can adiabatically switch from the ground state of the sector one Hamiltonian to the ground state of the sector two Hamiltonian by solving the time-dependent Schrödinger equation. In addition, by employing an initial wave packet orthogonal to that leading to the ground state of sector two, we also obtain the first-excited state of sector two. Construction of the orthogonal sector one states is trivial due to the tensor nature of sector two. The ground and first-excited states of the sector two Hamiltonian can be used with the charge operator to obtain the first two excited state wave functions of the sector one Hamiltonian. Excellent computational results are obtained for two-dimensional nonseparable degenerate and nondegenerate systems.     

Exact microscopic wave function for a topological quantum membrane

The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the noncommutative algebra on the four sphere. Our approach introduces a nonperturbative method to quantize topological membranes.     

A study on entanglement dynamics for a four-qubit model

In this paper, we consider the entanglement dynamics of a four-qubit model [2006 Phys. Rev. A 74 042328] where two entangled qubits a and b locally interact with separate qubits A and B via the spin-exchange-like Hamiltonian. We study the effect of purity of initial entangled state of qubits a, b on the entanglement evolution and its relation with energy transfer. Also, we find that the total bipartite entanglement of qubits a, b plus A, B is not a constant any longer when the initial entangled state of a, b is not pure, which is a complement to the result in the paper [2007 J. Phys. B 40 S45] for the pure case.     

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian.     

Quantum correlation in one-dimensional extended quantum compass model

We study the correlations in the one-dimensional extended quantum compass model in a transverse magnetic field. By exactly solving the Hamiltonian, we find that the quantum correlation of the ground state of one-dimensional quantum compass model is vanishing. We show that quantum discord can not only locate the quantum critical points, but also discern the orders of phase transitions. Furthermore, entanglement quantified by concurrence is also compared.     

Product-State Approximations to Quantum States

We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.     

Entanglement frustration for Gaussian states on symmetric graphs

We investigate the entanglement properties of multimode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constrains the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2D and 3D lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry.     

Entropic uncertainty for two atoms interacting with a cavity field under the influence of two photons (off-resonance case)

In this paper, we introduce a Hamiltonian model describing the interaction of two photons with two two-level atoms and a degenerate parametric amplifier. In the near-resonance case, we obtain an analytic solution of the evolution equation for the wave function in the Schr¨odinger picture and use the obtained result for discussing the atomic inversion, the purity, and the phenomenon of squeezing. We show that the phenomenon of superstructure appears in the atomic inversion in the presence of detuning (with parameter ??) and coupling (with parameter ??₃). Our study of the purity shows that the system is always in a mixed state, and the maximum value of entanglement occurs around ~0.6. Also we show that detuning leads to a reduction in the value of squeezing for all quadrature variances. In contrast, the coupling parameter leads to an increase in the value of squeezing. However, for the usual single-mode squeezing (of quadratures) the effect of detuning consists in increase in the squeezing period.     

On Isospectral Deformations of an Inhomogeneous String

For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the S-matrix from a single ground state wave function. Here, we define a class of Hamiltonians consisting of local commuting projectors and an associated matrix that is invariant under local unitary transformations. We argue that the invariant is equivalent to the topological S-matrix. The definition does not require degeneracy of the ground state. We prove that the invariant depends on the state only, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. As a corollary, we prove that any local quantum circuit that connects two ground states of quantum double models (discrete gauge theories) with non-isomorphic abelian groups must have depth that is at least linear in the system’s diameter. As a tool for the proof, a manifestly Hamiltonian-independent notion of locally invisible operators is introduced. This gives a sufficient condition for a many-body state not to be generated from a product state by any small depth quantum circuit; this is a many-body entanglement witness.     

Thermal entanglement in a triple quantum dot system

We present studies of thermal entanglement of a three-spin system in triangular symmetry. Spin correlations are described within an effective Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with super-exchange couplings modulated by an effective electric field. Additionally a homogenous magnetic field is applied to completely break the degeneracy of the system. We show that entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states. For the doublets with the same spin orientation one can observe nonmonotonic temperature dependence of entanglement due to competition between entanglement encoded in the ground state and the excited state. The mixing of the states with an opposite spin orientation or with quadruplets (unentangled states) always monotonically destroys entanglement. Pairwise entanglement is quantified using concurrence for which analytical formulae are derived in various thermal mixing scenarios. The electric field plays a specific role – it breaks the symmetry of the system and changes spin correlations. Rotating the electric field can create maximally entangled qubit pairs together with a separate spin (monogamy) that survives in a relatively wide temperature range providing robust pairwise entanglement generation at elevated temperatures.     

General entanglement scaling laws from time evolution

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.     

On Effectiveness of Protocol Creating Maximum Entanglement of Two Charge-Phase Qubits by Cavity Field

We revisit the protocols to create maximally entangled states between two Josephson junction （33） charge phase qubits coupled to a microwave field in a cavity as a quantum data bus. We analyze a novel mechanism of quantum decoherence due to the adiabatic entanglement between qubits and the data bus, the off-resonance microwave field. We show that even if the variable of the data bus can be adiabatically eliminated, the entanglement between the qubits and data bus remains and can decohere the superposition of two-particle state. Fortunately we can construct a decoherencefree subspace of two-dimension to against this adiabatic decoherence. To carry out the analytic study for this decoherence problem, we develop Frohlich transformation to re-derive the effective Hamiltonian of these systems, which is equivalent to that obtained from the adiabatic elimination approach.     

Entanglement and Sudden Death of a Nonlinear Two-Level-Atom Pair Interacting with a Radiation Field

We study the entanglement between a pair of two-level atoms simultaneously interacting via a singlemode thermal field. The Hamiltonian also describes a two-photon process. The entanglement between a nonlinear atom-field interacting system is also studied using atomic and field entropy changes. We use concurrence to detect the sudden death phenomenon. Furthermore, we discuss the relationship between entropy changes and concurrence entanglement. Our results show that the behavior of the entropy change is in agreement with the behavior of the concurrence when we measure the entanglement between the two-subsystem structure.