Signatures of fractional statistics in noise experiments in quantum Hall fluids

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.     

Entanglement of remote atomic qubits

We report observations of entanglement of two remote atomic qubits, achieved by generating an entangled state of an atomic qubit and a single photon at site , transmitting the photon to site in an adjacent laboratory through an optical fiber, and converting the photon into an atomic qubit. Entanglement of the two remote atomic qubits is inferred by performing, locally, quantum state transfer of each of the atomic qubits onto a photonic qubit and subsequent measurement of polarization correlations in violation of the Bell inequality [EQUATION: SEE TEXT]. We experimentally determine [EQUATION: SEE TEXT]. Entanglement of two remote atomic qubits, each qubit consisting of two independent spin wave excitations, and reversible, coherent transfer of entanglement between matter and light represent important advances in quantum information science.     

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.     

Quantum coherence and W∞ × SU(2) algebra in bilayer quantum Hall systems

We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-level projection taken into account. The symmetry group is found to be W_∞ × SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excitations are topological solitions in this coherent mode. We point out that they are detectable by measuring the Hall current distribution.     

Meta-Entanglement

We give a meta-logical interpretation of the entanglement mechanism of quantum space-time in terms of the sequent calculus of a quantum sub-structural logic. This meta-logical picture is based mainly on the two meta-rules cut and EPR, and on the new meta-theorem “teleportation” (TEL), built by the use of the above meta-rules, both performed in parallel. The proof of (TEL)-theorem fairly reproduces the protocol of quantum teleportation. In the framework of space-time entanglement, the conclusion of the (TEL)-theorem is that the entangled space-time can convey the quantum teleportation of an unknown quantum state. We also introduce two new structural rules: the Hadamard (H)-rule and the CNOT-rule, the latter being used, together with the cut, in the proof of the new theorem “Entanglement” (ENT).

     

Entanglement production with multimode Bose-einstein condensates in optical lattices

Deep optical lattices are considered, in each site of which there are many Bose condensed atoms. By the resonant modulation of trapping potentials, it is possible to transfer a macroscopic portion of atoms to the collective nonlinear states corresponding to topological coherent modes. Entanglement can be generated between these modes. By varying the resonant modulating field, it is possible to effectively regulate entanglement production in this multimode multitrap system of Bose condensates.     

Topological Numbers and Edge State of Hierarchical State in Rapidly Rotating Ultracold Atoms

The effective theory for the hierarchical fractional quantum Hall (FQH) effect is proposed. We also derive the topological numbers K matrix and t vector and the general edge excitation from the effective theory. One can find that the two issues in rapidly rotating ultracold atoms are similar to those in electron FQH liquid.     

Inelastic light scattering by collective excitations in the fractional quantum Hall regime

We report an inelastic light scattering study of long wavelength collective gap excitations of fractional quantum Hall (FQH) states at ν=p/(2p+1) for . The ν-dependence of the gap energy suggests a collapse of the collective excitation gap near . In a range of filling factors close to , where the FQH gap is believed to collapse, we observe a collective excitation mode that exists only at temperatures below 150 mK.     

Multi-types of Skyrmions in SU（N） Quantum Hall System

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

Entanglement Properties in Two-Component Bose-Einstein Condensate

We investigate entanglement inseparability and bipartite entanglement of in two-component Bose-Einstein condensate in the presence of the nonlinear interatomic interaction, interspecies interaction. Entanglement inseparability and bipartite entanglement have the similar properties. More entanglement can be generated by adjusting the nonlinear interatomic interaction and control the time interval of the entanglement by adjusting interspecies interaction.     

Entanglement Properties of Two-Mode Squeezed Coherent States in Radiation Field

Entanglement properties of two-mode squeezed coherent states in the radiation field are investigated according to the entanglement criterion [Phys. Rev. Lett. 84 (2000) 2722]. The dependence of entanglement on squeeze angle and squeeze parameter is discussed. It shows that the system evolves into entangled states and entanglement does not increase persistently with the increase of squeeze angle and squeeze parameter. There only exists a certain squeeze angle in which the entanglement exists continuously.     

Integer and fractional quantum Hall effects in bilayer electron systems

Integer and fractional quantum Hall (QH) effects are studied in bilayer electron systems both theoretically and experimentally, especially, at ν=2 and 2/3. Due to the spin and layer degrees of freedom, the SU(4) symmetry underlies the integer QH states, where quantum coherence develops spontaneously and quasiparticles are coherent excitations. It is intriguing that a pair of skyrmions makes one quasiparticle at ν=2. In the fractional QH regime, on the other hand, the composite-fermion cyclotron gap competes with the Zeeman and tunneling gaps, bringing in new phases and excitations. At ν=2/3 our experimental data suggest that a quasiparticle is not a coherent excitation but simply a composite fermion.     

Entanglement Purification of Noisy Two-Qutrit States Via Environment Measurement

Entanglement swapping combined with environment measurement is proposed to purify entanglement of two-qutrit entangled states subjected to the local individual amplitude damping channels. The resultant states of our scheme have much more entanglement even though entanglement swapping itself cannot purify entanglement. When the scheme is applied to dense coding, the dense coding capacity can be significantly improved.     

Multi-copy entanglement purification with practical spontaneous parametric down conversion sources

Entanglement purification is to distill the high quality entanglement from the low quality entanglement with local operations and classical communications. It is one of the key technologies in long-distance quantum communication. We discuss an entanglement purification protocol(EPP) with spontaneous parametric down conversion(SPDC) sources, in contrast to previous EPP with multi-copy mixed states, which requires ideal entanglement sources. We show that the SPDC source is not an obstacle for purification, but can benefit the fidelity of the purified mixed state. This EPP works for linear optics and is feasible in current experiment technology.     

The entanglement dynamics of two coupled qubits in different environment

In this Letter, the entanglement dynamics of two interacting qubits in a common bath and in two independent baths, at finite and zero temperature are investigated. Entanglement sudden death (ESD) and entanglement sudden birth (ESB) are observed when the two qubits are embedded in two independent baths at finite temperature. At zero temperature, the entanglement of the two qubits may evolve to a steady state with non-zero value when the two qubits are embedded in a common bath, the entanglement sudden birth does not occur when the qubits are embedded in two independent baths.     

Entanglement for Two Dissipative Qubits

Entanglement dynamics of two qubits from environmental perturbations with different initial conditions is investigated. The results show that the qubit-qubit interaction leads to a periodic disentanglement and entanglement. It is surprised that the sudden death of entanglement (ESD) does not happen for non-interacting qubits, but for both the cases of a pure dephasing environment and a normal environment, ESD emerges. The results may provide a useful clue to implement an entanglement quantum information.     

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.     

Separability of evolving W state in a noise environment

Entanglement is an important resource for quantum information processing. We provide a new entanglement witness to detect the entanglement of an evolving W state. Our results show that the new entanglement witness matches the evolving W state better than other witnesses or methods. The new witness significantly improves the performance of entanglement detection for some three-qubit states.     

Virtual Excitations and Entanglement Dynamics and Polygamy in Three Ultra-Strongly Coupled Systems

The Milburn dynamics of three non resonant ultra-strongly coupled oscillators are resolved by using symplectic geometry. The Milburn dynamics of virtual excitations and how they affect the pairwise entanglement are looked at. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, it is shown that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, the effects of physical parameters on the redistribution of virtual excitations among the three bi-partitions are analyzed. As a result, the violation of the monogamy of excitations is shown as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, it is emphasized that the treatment can be used to model coupled quantum circuits in real situations (with decoherence).