Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session J15: Quantum Entanglement |
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Sponsoring Units: GQI Chair: Christopher Fuchs, Perimeter Institute Room: 316 |
Tuesday, March 17, 2009 11:15AM - 11:27AM |
J15.00001: Understanding Entanglement as a Resource for Quantum Information Processing Scott M. Cohen Ever since Erwin Schrodinger shocked the physics world by killing (and not killing) his cat, entanglement has played a critical role in attempts to understand quantum mechanics. More recently, entanglement has been shown to be a valuable resource, of central importance for quantum computation and the processing of quantum information. In this talk, I will describe a new diagrammatic approach to understanding why entanglement is so valuable, the key idea being that entanglement between two systems ``creates'' multiple images of the state of a third. By way of example, I will show how to ``visualize'' teleportation of unknown quantum states, and how to use entanglement to determine the (unknown) state of a spatially distributed, multipartite quantum system. Illustrative examples of this entanglement-assisted local state discrimination are sets of orthogonal product states exhibiting what is known as ``non-locality without entanglement'', including unextendible product bases. These ideas have also proven useful in using entanglement to implement a unitary interaction between spatially separated (and therefore non-interacting!) systems. [Preview Abstract] |
Tuesday, March 17, 2009 11:27AM - 11:39AM |
J15.00002: Genuine tripartite entanglement and nonlocality in 3-qubit GHZ-class states Shohini Ghose, Neil Sinclair, Shantanu Debnath, Rene Stock, Pranaw Rungta Multiqubit entanglement is a crucial ingredient for large-scale quantum information processing and has been the focus of several recent studies. Entanglement between qubits can lead to violations of Bell-type inequalities that are satisfied by local hidden variable models, indicating the nonlocal nature of the correlations between qubits. For 2-qubit pure states, bipartite entanglement is simply related to the Bell-CHSH nonlocality parameter. No such analytical relation between multipartite entanglement and nonlocality has yet been obtained for systems of three or more qubits. We have derived relationships between genuine tripartite entanglement and nonlocality for families of 3-qubit GHZ-class pure states. We quantify tripartite entanglement by the 3-tangle and derive its relationship to the Svetlichny inequality for testing tripartite nonlocality. For the class of generalized GHZ states, although the 3-tangle is always non-zero, we identify some states that do not violate the Svetlichny inequality. Furthermore, we show that states known as the maximal slice states always violate the Svetlichny inequality and analogous to the 2-qubit case, the amount of violation increases with the 3-tangle. The generalized GHZ states and the maximal slice states have unique tripartite entanglement and nonlocality properties in the set of all pure states. [Preview Abstract] |
Tuesday, March 17, 2009 11:39AM - 11:51AM |
J15.00003: Quantum Noise as an Entanglement Entropy Meter. Israel Klich, Leonid Levitov Entanglement entropy, which is a measure of quantum correlations between separate parts of many-body system, is defined solely in terms of the many-body density matrix, with no relation to any particular observables. Because of that, it has not been clear how to access this quantity experimentally. Here we unveil a universal relation between entanglement entropy of fermions and statistics of current flowing through a quantum point contact. This relation provides a way to experimentally measure entanglement entropy, and test seminal results of conformal field theory such as the prediction of Holzhey, Larsen and Wilczek for entanglement entropy of fermions. [Preview Abstract] |
Tuesday, March 17, 2009 11:51AM - 12:03PM |
J15.00004: Coherent Light Fields for Entanglement based Quantum Communication Kim Fook Lee Nonlocal polarization correlations of two distant observers based on Stapp's formulation are observed by using coherent light fields. Using a 50/50 beam splitter transformation, a vertically polarized coherent light field is entangled with a horizontally polarized coherent noise field. The superposed light fields at each output port of the beam splitter are sent to two distant observers, where the fields are interfered and manipulated at each observer by using a quarter wave plate and an analyzer. The interference signal contains information of the projection angle of the analyzer, which is hidden by the phase noises. The nonlocal correlations between the projection angles of two distant observers are established by analyzing their data through analog signal multiplication without any post-selection technique. This scheme can be used to implement Ekert's protocol for quantum key distribution. The implementation of two independent coherent states in this scheme is also discussed. [Preview Abstract] |
Tuesday, March 17, 2009 12:03PM - 12:15PM |
J15.00005: Quantum-entanglement aspects of polaron systems Vladimir Stojanovic, Mihajlo Vanevic We describe quantum entanglement inherent to the polaron ground states of coupled electron-phonon (or, more generally, particle- phonon) systems based on a model comprising both local (Holstein-type) and nonlocal (Peierls-type) coupling. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particle-phonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particle-phonon entanglement. In particular, we find a compelling evidence for the existence of a non-analyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such non-analyticity -- not accompanied by an actual quantum phase transition -- reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantum- dissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the self-trapped region where the small-polaron states are nearly maximally mixed. [Preview Abstract] |
Tuesday, March 17, 2009 12:15PM - 12:27PM |
J15.00006: Entanglement genesis under continuous parity measurement Andrew Jordan We examine the stochastic dynamics of entanglement for an uncoupled two-qubit system, undergoing continuous parity measurement. Starting with a fully mixed state, the entanglement is zero for a finite amount of time, when it is suddenly created, which we refer to as entanglement genesis. There can be further entanglement sudden death/birth events culminating in the formation of a fully entangled state. We present numerical investigations of this effect together with statistics of the entanglement genesis time in the weak measurement limit as well as the quantum Zeno limit. An analytic treatment of the physics is presented, aided by the derivation of a simple concurrence equation for Bell basis X-states. The probability of entanglement border crossing and mean first passage times are calculated for the case of measurement dynamics alone. We find that states with almost the same probability of entanglement border crossing can have very different average crossing times. Our results provide insights on the optimization of entanglement generation by measurement. Reference: N. S. Williams and A. N. Jordan, arXiv:0809.3248 [Preview Abstract] |
Tuesday, March 17, 2009 12:27PM - 12:39PM |
J15.00007: Interferometric Determination of Concurrence of Unknown Two-Qubit Entanglement S.-S. B. Lee, H.-S. Sim We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved, by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. For some representative quantum states, the efficiency is compared between our interferometric scheme and the full state tomography. For some states, our scheme is revealed to be more efficient than the tomography. [Preview Abstract] |
Tuesday, March 17, 2009 12:39PM - 12:51PM |
J15.00008: Scattering approach to the entanglement entropy area law for fermions Gregory Levine The entanglement entropy (EE) of a critical fermion system coupled to another system by a ``weak link'' is studied perturbatively in the weak link amplitude, $w$. In this model, EE arises from $s$-wave scattering connecting the two subsystems and is computed from perturbative corrections to the subsystem correlation function. The first non-vanishing contribution to the EE, appearing at $O(w^2)$, may be evaluated analytically and is shown to diverge as $w^2 \ln^2{L}$, where $L$ is the linear subsystem size. A generalized version of this model containing many independent weak links is discussed in connection with the entropy area law for fermions. [Preview Abstract] |
Tuesday, March 17, 2009 12:51PM - 1:03PM |
J15.00009: Mutual information and compactification radius in a c=1 critical phase in one dimension Shunsuke Furukawa, Vincent Pasquier, Jun'ichi Shiraishi We investigate the generic scaling of the mutual information in a class of one-dimensional quantum critical systems described by a bosonic field theory with a central charge $c=1$. A numerical analysis of a spin-chain model reveals that the mutual information is scale-invariant and depends on the compactification radius (or the Tomonaga-Luttinger parameter) of the bosonic field, as opposed to the general prediction of Calabrese and Cardy. Interpretations of the results are given in terms of branch-point twist fields. The present study provides a new way to determine the compactification radius, and furthermore demonstrates the ability of the mutual information to distinguish different conformal field theories with the same central charge. [Preview Abstract] |
Tuesday, March 17, 2009 1:03PM - 1:15PM |
J15.00010: Universal behavior of the entanglement entropy in 2D conformal quantum critical points and generalized quantum dimer models Benjamin Hsu, Michael Mulligan, Eduardo Fradkin, Eun-Ah Kim We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, {\it i.e.\/} systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system has a universal contribution which is independent of the size of the region. This universal contribution is computable in terms of the properties of the underlying large-scale conformal structure of the wave function of these quantum critical systems. [Preview Abstract] |
Tuesday, March 17, 2009 1:15PM - 1:27PM |
J15.00011: Theory of finite-entanglement scaling at one-dimensional quantum critical points Frank Pollmann, Subroto Mukerjee, Ari Turner, Joel Moore We present a quantitative scaling theory of finite-entanglement approximations at one-dimensional quantum critical points. Finite-entanglement scaling is governed not by the scaling dimension of an operator but by the ``central charge'' of the critical point, which counts its universal degrees of freedom. An important ingredient is the universal distribution of density-matrix eigenvalues (the ``entanglement spectrum'') at a critical point recently obtained by Calabrese and Lefevre. The theory is compared to the numerical error scaling of several quantum critical points, obtained by the infinite Time Evolved Block Decimation (iTEBD) method that extends the conventional Density-Matrix Renormalization Group (DMRG) algorithm. [Preview Abstract] |
Tuesday, March 17, 2009 1:27PM - 1:39PM |
J15.00012: ABSTRACT WITHDRAWN |
Tuesday, March 17, 2009 1:39PM - 1:51PM |
J15.00013: Entanglement under the renormalization-group transformations on quantum states and in quantum phase transitions Tzu-Chieh Wei We consider the entanglement of states under the renormalization-group (RG) transformations and apply it to the ground states of Hamiltonians that possess quantum phase transitions. We find that near critical points, the ground-state entanglement under RG transformation exhibits singular behavior. The singular behavior under finite steps of RG reveals the correlation length exponent. However, under the infinite steps of RG transformation, the singular behavior is rendered different, and it is not universal unless the critical point can be described by a conformal field theory. [Preview Abstract] |
Tuesday, March 17, 2009 1:51PM - 2:03PM |
J15.00014: Comparisons of entanglement witnesses for n-qubit systems Richard Bonde, Andrew Schauf, Elizabeth Behrman An overlooked problem in witness design is the possibility of phase offset contamination. For example, the singlet EPS 2-qubit state $\frac{1}{\sqrt 2 }\left( {\left| {\uparrow \downarrow } \right\rangle -\left| {\downarrow \uparrow } \right\rangle } \right)$differs from $\frac{1}{\sqrt 2 }\left( {\left| {\uparrow \downarrow } \right\rangle +\left| {\downarrow \uparrow } \right\rangle } \right)$only by a relative phase factor of $e^{i\pi }$, yet both states are fully entangled. We compare in detail several published witnesses on entangled pure and mixed systems with varying degrees of phase offset. [Preview Abstract] |
Tuesday, March 17, 2009 2:03PM - 2:15PM |
J15.00015: ABSTRACT WITHDRAWN |
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