Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session A40: Quantum Entanglement |
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Sponsoring Units: TGQI DCMP Chair: Christopher Fuchs, Bell Labs & Lucent Technologies Room: Baltimore Convention Center 343 |
Monday, March 13, 2006 8:00AM - 8:12AM |
A40.00001: A set of entanglement monotones for characterising experimental data Peter Love, Alec Maassen van den Brink, Mohammed Amin, Anatoly Smirnov, Miroslav Grajcar, Evgeni Il'ichev, Andrei Izmalkov, Alex Zagoskin We define a set of elementary entanglement monotones and give a single measure of entanglement in terms of these monotones which is zero except on globally entangled states. We compute this measure for the ground state of a four qubit superconducting experimental system, and thus confirmed the presence of genuine four-qubit entanglement in the ground state. [Preview Abstract] |
Monday, March 13, 2006 8:12AM - 8:24AM |
A40.00002: Dynamic learning of an experimental entanglement witness for an n-qubit system Kathleen Walsh, Elizabeth Behrman, James Steck, Steven Skinner We extend our previous work on dynamic learning of an entanglement witness for a two-qubit system to n qubits, and show detailed comparisons for the two- and three-qubit systems to published entanglement measures. Our method can also be used for quNits, and can handle a small amount of noise and decoherence. [Preview Abstract] |
Monday, March 13, 2006 8:24AM - 8:36AM |
A40.00003: Dynamics and scaling of multi-partite entanglement Florian Mintert We derive reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. This allows us to define a life time of entanglement for different realistic experimental scenarios, and investigate its scaling behaviour with increasing system size. [Preview Abstract] |
Monday, March 13, 2006 8:36AM - 8:48AM |
A40.00004: The entanglement entropy and the Berry phase in solid states Shinsei Ryu, Yasuhiro Hatsugai The entanglement entropy (von-Neumann entropy) has been used to characterize the quantum entanglement of many-body ground states in strongly correlated systems. In this talk, we try to establish a connection between the lower bound of the von-Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of 1D Hamiltonians with two bands separated by a finite gap is investigated. We argue that when the Berry phase (Zak's phase) of the occupied band is equal to $\pm \pi \times (\mbox{odd integer})$ and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than $\ln 2$ (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two spins. We also discuss it is related to vanishing of the expectation value of a certain non-local operator which creates a kink in 1D systems. [Preview Abstract] |
Monday, March 13, 2006 8:48AM - 9:00AM |
A40.00005: Multiparticle interference, GHZ entanglement, and full counting statistics Heung-Sun Sim, Eugene V. Sukhorukov We study [1] quantum coherent transport in a generalized $N$-particle Hanbury Brown-Twiss setup enclosing magnetic flux, where electrons are injected from $N$ independent sources and collected in $N$ distant detectors, and show that the $N$-th order cumulant of current cross correlations exhibits flux-dependent periodic Aharonov-Bohm (AB) oscillations, while there is no such oscillation in all the lower-order cumulants. The origin of the multiparticle interference is the orbital Greenberger-Horne-Zeilinger entanglement of $N$ identical particles. For sufficiently strong AB oscillations the generalized $N$-particle Bell inequalities may be violated, proving the $N$-particle quantum nonlocality.\newline \newline [1] H.-S. Sim and E. V. Sukhorukov, condmat/0508399. [Preview Abstract] |
Monday, March 13, 2006 9:00AM - 9:12AM |
A40.00006: Correlations in a multi-qubit state D.L. Zhou, B. Zeng, Z. Xu, L. You For an arbitrary partition of a multi-qubit system, we define a correlation measure, which is directly based on a series of multi-qubit correlation functions, to characterize the total correlation among different parts. As an instructive application of our correlation measures, we investigate the entanglement of graph states. [Preview Abstract] |
Monday, March 13, 2006 9:12AM - 9:24AM |
A40.00007: Entanglement of overlapping systems and the breakdown of the tensor product Matthew Leifer Recent work on entanglement in the presence of superselection rules has shown that entanglement ought to be defined operationally, i.e. with respect to sets of local operations actually available to Alice and Bob rather than with respect to an arbitrary tensor product factorization of the state space. Usually Alice and Bob's local operations are assumed to commute, which is an appropriate assumption when their systems are well separated. In this talk I address the question of how far the usual formalism can be maintained if the local operations do not commute. This might be an appropriate description of the spin entanglement between two particles with overlapping spatial wavefunctions, since local operations might then have an effect on both spins. In this situation, the appropriate notion of entanglement is no longer associated to a tensor product factorization of the state space, but it can be approximated by one provided the overlap of the two systems is small and/or the preparable states are sufficiently mixed. In this talk I will present a simple model of the breakdown of the tensor product for two qubits, characterize the states that need to be prepared to observe the effect and discuss how the observed entanglement is related to the entanglement with respect to the usual tensor product factorization. [Preview Abstract] |
Monday, March 13, 2006 9:24AM - 9:36AM |
A40.00008: Modelling Pauli measurements on arbitrary stabilizer states via local hidden variables assisted by classical communication Matthew Elliott, Bryan Eastin, Carlton Caves, Jonathan Barrett, Stefano Pironio In this talk I present communication-assisted local-hidden-variable models for measurements of products of Pauli matrices on stabilizer states. Models are analyzed with respect to restrictions imposed and their efficacy in predicting overall measurement outcomes as well as outcomes of correlated subsets of measurements. In particular, I present a model in which the quantum mechanical results of Pauli product measurements can be predicted by a local-hidden-variable table supplemented by an efficient amount of classical communication and computation. [Preview Abstract] |
Monday, March 13, 2006 9:36AM - 9:48AM |
A40.00009: Quantum Chaos, Localization, and Entanglement in Disordered Heisenberg Models Winton Brown, David Starling, Lea Santos, Lorenza Viola We explore the relation between quantum chaos, localization, and entanglement in a two-dimensional disordered Heisenberg spin-1/2 system. Apart from the recent interest in such systems as models for proposed quantum computing architectures, they exhibit interesting transition regions from integrability to chaos and from higher to lower degree of symmetry. Complementing the standard eigenvalue-based analysis for identifying the cross-over into chaos, we suggest looking at the relative delocalization of eigenvectors related to different disorder realizations as a basis-independent indicator of chaoticity. We investigate the behavior of several measures of bipartite and multipartite entanglement -- including concurrence; von Neumann entropy; and, using the framework of generalized entanglement, a family of local purities. Our results indicate that bipartite entanglement decreases in the chaotic region, whereas the opposite holds for multipartite entanglement. Connections are established with predictions from random matrix theory. [Preview Abstract] |
Monday, March 13, 2006 9:48AM - 10:00AM |
A40.00010: Entanglement Scaling at Quantum Phase Transitions in Correlated Electron Systems Daniel Larsson, Henrik Johannesson We have carried out an analytic study of the entanglement scaling properties in the one-dimensional Hubbard model. We present exact scaling formulas for the local ("single-site") entanglement $\mathcal{E}$ at a quantum phase transition driven by a magnetic field or a chemical potential. The leading divergences of $d\mathcal{E}$/$dh$ and $d\mathcal{E}$/$d\mu$ are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections signal a change in the number of local states accessible to the system as it undergoes the transition. We show that the results for the leading divergences are generic, and follow from the scaling hypothesis that any local observable exhibits a singularity at a quantum phase transition. Illustrations from other strongly correlated electron systems are given, including the long-range Hubbard model in one dimension. [Preview Abstract] |
Monday, March 13, 2006 10:00AM - 10:12AM |
A40.00011: Coherent Interaction of Spins Induced by Thermal Bosonic Environment. Denis Tolkunov, Dmitry Solenov, Vladimir Privman We obtain the indirect exchange interaction between two two-state systems, e.g., spins, in a formulation that also incorporates the quantum noise that they experience, due to an environment of bosonic modes, for instance, phonons. We predict that for low enough temperatures the interaction is coherent over time scales sufficient to create entanglement, dominated by the zero-point quantum fluctuations of the environment. We utilize a perturbative approach to obtain a quantum evolution equation for the two-spin dynamics. The induced interaction is calculated exactly. We identify the time scales for which the spins develop and sustain entanglement for various spatial separations. [Preview Abstract] |
Monday, March 13, 2006 10:12AM - 10:24AM |
A40.00012: Entanglement entropy of random quantum critical points with general spin Joel Moore, Gil Refael The bipartite entanglement at 1D critical points of a subsystem of $N$ sites with the remainder is known to diverge as $\log N$, with a coefficient that is related to the central charge for conformally invariant critical points. It was recently shown that for a class of spin-half random critical points, there is also a logarithmic divergence with a coefficient that is universal and corresponds to an irrational ``effective central charge.'' This talk discusses generalizations of this result to higher-spin chains, including the permutation-symmetric critical points found by Damle and Huse, using a combination of analytic and numerical real-space renormalization group methods. Higher-spin chains show numerous complications relative to the spin-half case, such as the introduction of ferromagnetic bonds; their study provides a stringent test of the conjectured $c$-theorem for central charges defined via entanglement entropy. [Preview Abstract] |
Monday, March 13, 2006 10:24AM - 10:36AM |
A40.00013: Local Entanglement and Quantum Phase Transition in Spin Models Shi-Jian Gu, Guang-Shan Tian, Hai-Qing Lin In this work, we study quantum phase transitions in both the one- and two-dimensional XXZ models with either spin $S$=1/2 or $S$=1 by a local entanglement We show that the behavior of $E_{v}$ is dictated by the low-lying spin excitation spectra of these systems. Therefore, the anomalies of $E_{v}$ determine their critical points. It reminds us the well-known fact in optics: The three-dimensional image of one subject can be recovered from a small piece of holograph, which records interference pattern of the reflected light beams from it. Similarly, we find that the local entanglement, which is rooted in the quantum superposition principle, provides us with a deep insight into the long-range spin correlations in these quantum spin systems. \textbf{References:} [1] S. Sachdev, \textit{Quantum Phase Transitions} (Cambridge University Press, Cambridge, 2000). [2] Shi-Jian Gu, Guang-Shan Tian, and Hai-Qing Lin quant-ph/0509070 [Preview Abstract] |
Monday, March 13, 2006 10:36AM - 10:48AM |
A40.00014: Quantum Entanglement in a Spin Ladder with Ring Exchange Jun-Liang Song, Shi-Jian Gu, Hai-Qing Lin In this paper we've studied entanglement properties of a spin ladder with ring exchange. Several entanglement properties, e.g. pair concurrence and block-block entanglement were obtained by exact diagonalization method. The relationship between the global phase diagram and ground-state quantum entanglement was investigated. It was shown that block-block entanglement of different block size and configurations manifests richer information of the system. It was also found that the block-block entanglement reaches its maximum or minimum at some QPT points which is also the high symmetry point. The temperature dependence of the entanglement properties is also investigated and it is shown that entanglement is suppressed by the temperature fluctuations and vanishes at some threshold temperatures. [Preview Abstract] |
Monday, March 13, 2006 10:48AM - 11:00AM |
A40.00015: Entanglement and dissipation in a quantum-dot array. Lesvia Debora Contreras-Pulido, Fernando Rojas, Ramon Aguado Primarily motivated by quantum information theory, charge in quantum dots (QD) seems to be a promising candidate for implementation of qubits and entangled states [1]. We explore theoretically the dynamical formation of entangled states, including dissipative effects, of two parallel double QD uncoupled between them but strongly coupled to the same phonon thermal bath. The QD array is modeled with an extended Hubbard type Hamiltonian and dissipation is taken into account by using a polaron transformation to obtain the reduced density matrix of the system [2]. We find that it is possible to obtain entangled electronic states through a strong electron-phonon interaction, characterized by: Wootters' concurrence, charge distribution and probabilities for each Bell state as a function of relevant parameters (hopping, temperature, electron-phonon amplitude). The work is supported by DGAPA project IN114403 and CONACyT project 43673-F [1] Hichri et al., Phys.E 24,234 (2004) [2] Aguado and Brandes, Phys.Rev.Lett.92, 206601 (2004). [Preview Abstract] |
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