Low Entanglement Research Articles

Wick's theorem for matrix product states.

Matrix product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method and continuous variants thereof. In this work we show that, generically, N-point functions of arbitrary operators in discrete and continuous translation invariant matrix product states are completely characterized by the corresponding two- and three-point functions. Aside from having important consequences for the structure of correlations in quantum states with low entanglement, this result provides a new way of reconstructing unknown states from correlation measurements, e.g., for one-dimensional continuous systems of cold atoms. We argue that such a relation of correlation functions may help in devising perturbative approaches to interacting theories.

Backreacting p-wave superconductors

We study the gravitational backreaction of the non-abelian gauge field on the gravity dual to a 2+1 p-wave superconductor. We observe that as in the $p+ip$ system a second order phase transition exists between a superconducting and a normal state. Moreover, we conclude that, below the phase transition temperature $T_c$ the lowest free energy is achieved by the p-wave solution. In order to probe the solution, we compute the holographic entanglement entropy. For both $p$ and $p+ip$ systems the entanglement entropy satisfies an area law. For any given entangling surface, the p-wave superconductor has lower entanglement entropy.

Pelagic longline fishing trials to shape a mitigation device of the depredation by toothed whales

Depredation is defined as the damage or removal of fish from fishing gear by predators, and is a crucial issue leading to negative impacts on both animals involved in depredation and fisheries. Depredation in longline pelagic fisheries targeting swordfish (Xiphias gladius) and tuna (Thunnus spp.) involves short-finned pilot whales (Globicephala macrorhynchus), false killer whales (Pseudorca crassidens) and some pelagic sharks. Since no long-term solution could be found to date, we investigated fishing gear improvement by deploying a technology designed to physically protect the hooked fish by hiding it to predators: the DMD (depredation mitigation device). Two types of DMDs were designed: “spiders” and “socks”. The efficiency of “spiders” was tested in November 2007 during a fishing trial of 26 longline fishing operations when 12,480 hooks and 1970 devices were set. The efficiency of “socks” was tested in October 2008 during a fishing trial of 32 longline fishing operations when 13,220 hooks and 339 devices were set. 117 and 24 fish were hooked on branchlines equipped with spiders and socks, respectively and among those devices, 87.3% versus 69.2% were correctly triggered and 80% versus 15% of the fish were correctly protected. A low entanglement rate of the spiders with the fishing gear was found (3.6%), but a higher one was associated to the socks (17.8%). Operational constraints to routinely deploy “spiders” were examined. The number of sets impacted by shark depredation was significantly greater than the number of sets involving toothed whale depredation. However, when depredation occurred, the proportion of fish damaged by toothed whales was significantly greater. While more trials should be carried out to deeply verify the efficiency of DMDs, we remain convinced that considerations of fishing gear technologies might be more actively investigated to propose innovative measures to mitigate toothed whale depredation in pelagic longlining. For this type of gear, innovative technology is an important issue of the ecosystem approach to fisheries (EAF) framework.

Conformal field theory approach to Fermi liquids and other highly entangled states

The Fermi surface may be usefully viewed as a collection of 1+1 dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground state properties of the Fermi gas including entanglement entropy and number fluctuations. The 1+1 dimensional picture also generalizes to finite temperature and the presence of interactions. Finally, I argue that the low energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface.

Low entanglement wavefunctions

AbstractWe review a class of efficient wavefunction approximations that are based around the limit of low entanglement. These wavefunctions, which go by such names as matrix product states and tensor network states, occupy a different region of Hilbert space from wavefunctions built around the Hartree–Fock limit. The best known class of low entanglement wavefunctions, the matrix product states, forms the variational space of the density matrix renormalization group algorithm. Because of their different structure to many other quantum chemistry wavefunctions, low entanglement approximations hold promise for problems conventionally considered hard in quantum chemistry, and in particular problems which have a multireference or strong correlation nature. In this review, we describe low entanglement wavefunctions at an introductory level, focusing on the main theoretical ideas. Topics covered include the theory of efficient wavefunction approximations, entanglement, matrix product states, and tensor network states including the tree tensor network, projected entangled pair states, and the multiscale entanglement renormalization ansatz. © 2012 John Wiley & Sons, Ltd.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Influence of the tert‐dodecyl mercaptan content in poly(acrylonitrile‐butadiene‐styrene) on properties of chlorinated polyvinyl chloride/poly(acrylonitrile‐butadiene‐styrene) blends

AbstractA series of poly(acrylonitrile‐butadiene‐styrene) (ABS) grafting modifiers were synthesized by emulsion grafting poly(acrylonitrile‐styrene) (SAN) copolymer onto polybutadiene (PB) latex rubber particles. The chain transfer reagent tert‐dodecyl mercaptan (TDDM) was used to regulate the grafting degree of ABS and the molecular weight of SAN copolymers. By blending these ABS modifiers with Chlorinated polyvinyl chloride (CPVC) resin, a series of CPVC/ABS blends were obtained. The morphology, compatibility, and the mechanical properties of CPVC/ABS blends were investigated. The scanning electron microscope (SEM) studies showed that the ABS domain all uniformly dispersed in CPVC matrix. Dynamic mechanical analyses (DMA) results showed that the compatibility between CPVC and SAN became enhanced with the TDDM content. From the mechanical properties study of the CPVC/ABS blends, it was revealed that the impact strength first increases and then decreases with the TDDM content, which means that the compatibility between CPVC and the SAN was not the only requirement for maximizing toughness. The decreasing of tensile strength and the elongations might attribute to the lower entanglement between chains of CPVC and SAN. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

Reducing memory cost of exact diagonalization using singular value decomposition

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, without restricting to variational ansatzes. The lattice of size N is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of n(svd) smaller subcluster vectors using singular value decomposition. For low entanglement entropy S(ee), (satisfied by short-range Hamiltonians), the truncation error is expected to vanish as exp(-n(svd)(1/S(ee))). Convergence is tested for the Heisenberg model on Kagomé clusters of 24, 30, and 36 sites, with no lattice symmetries exploited, using less than 15 GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.

Large Violation of Bell Inequalities with Low Entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order $${\frac{\sqrt{n}}{\log n}}$$ with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.

High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement

Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use. It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states. We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length. Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is. These families of EAQECCs that are constructed from classical finite geometric LDPC codes perform very well according to our numerical simulations. Our work indicates that EAQECCs are not only theoretically interesting, but also physically implementable. Finally, these high performance entanglement-assisted LDPC codes with low entanglement consumption rates allow one to construct high-performance standard QECCs with very similar parameters.

SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. A fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called W1 + ∞. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern–Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU(m) quarks, where m is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the ν = 2/5 fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.

Preparation and Characterization of an Oxidized MWCNT-Reinforced Nafion<SUP>®</SUP> Nanocomposite Membrane for Direct Methanol Fuel Cell

Oxidized multiwalled carbon nanotube (MWCNT) reinforced Nafion ® nanocomposite membranes were prepared toward the use a polymer electrolyte membrane (PEM) for direct methanol fuel cells. To reduce methanol crossover through Nafion ® membrane, the oxidized MWCNTs were prepared and added into the Nafion ® membrane in the range of 0.5―3 wt%. The oxidized MWCNTs were prepared by treatment with 60% nitric acid at 120 ° C for 12 h and characterized by scanning electron microscope and Raman spectroscopy. Well-aligned structures with low entanglement were observed in the oxidized MWCNTs. The portion of amorphous carbon structure in the oxidized MWCNTs was increased by the oxidation reaction. The oxidized MWCNT reinforced Nafion ® nanocomposite membranes were prepared by a solution casting method on a hot plate. Thermal stability was enhanced by adding MWCNT into Nafion ® membranes. While MWCNT-reinforced Nafion ® nanocomposite membranes exhibited similar ion exchange capacity to that of Nafion ® , the methanol uptake was reduced about 14 wt%.

Competition between Shear Banding and Wall Slip in Wormlike Micelles

The interplay between shear band (SB) formation and boundary conditions (BC) is investigated in wormlike micellar systems (CPyCl-NaSal) using ultrasonic velocimetry coupled to standard rheology in Couette geometry. Time-resolved velocity profiles are recorded during transient strain-controlled experiments in smooth and sandblasted geometries. For stick BC standard SB is observed, although depending on the degree of micellar entanglement temporal fluctuations are reported in the highly sheared band. For slip BC wall slip occurs only for shear rates larger than the start of the stress plateau. At low entanglement, SB formation is shifted by a constant Delta gamma, while for more entangled systems SB constantly "nucleate and melt." Micellar orientation gradients at the walls may account for these original features.

Quantum repeaters using coherent-state communication

We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.

Measurement-Based Entanglement under Conditions of Extreme Photon Loss

The act of measuring optical emissions from two remote qubits can entangle them. By demanding that a photon from each qubit reaches the detectors, one can ensure that no photon was lost. But retaining both photons is rare when loss rates are high, as in Moehring et al. where 30 successes occurred per 10(9) attempts. We describe a means to exploit the low grade entanglement heralded by the detection of a lone photon: A subsequent perfect operation is quickly achieved by consuming this noisy resource. We require only two qubits per node, and can tolerate both path length variation and loss asymmetry. The impact of photon loss upon the failure rate is then linear; realistic high-loss devices can gain orders of magnitude in performance and thus support quantum computing.

Deterministic dense coding and entanglement entropy

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of nonmaximally entangled qudits in a pure state |{psi}>. Our results include the following: (i) We prove that it is possible for a state |{psi}> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d=3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d+j messages, 2{ allows the sending of K messages and has {radical}({lambda}{sub 0}) as its largest Schmidt coefficient, we show that the inequality {lambda}{sub 0}{<=}d/K, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form {lambda}{sub 0}<d/K if K=d+1, while our constructions of local unitaries show that equality canmore » be realized if K=d+2 or K=2d-1.« less

Nonlinear viscoelastic response of dendritic (arborescent) polyisobutylenes in single- and reversing double-step shearing flows

Single-step and three types of reversing double-step experiments were conducted on concentrated solutions of a linear and two dendritic (hyperbranched or arborescent) polyisobutylenes (PIBs). The results in reversing double-step experiments further confirm our previous findings on polyethylene melts that the K-BKZ theory provides better predictions for long chain branched polymers than linear ones. The short chain branched material looks more like the linear material in the present experiments. Isochronal derivatives of the strain potential function (W1 and W2) were calculated from torque (T) and normal force (N) responses in single-step parallel plate experiments. The damping function was extracted from W1 and W2 for both linear and branched PIBs. The damping function of the linear PIB falls between two versions of the Doi–Edwards model. The arborescent PIB with longer branches and lower branching frequency shows weak damping behavior, which is a specific behavior for long chain branched polymers. The arborescent PIB with shorter branches, higher branching frequency and low entanglement density, on the other hand, exhibits the same damping behavior as that of the linear PIB, which is consistent with the findings in the reversing double-step experiments in which it behaves more like a linear polymer.

Assessment of weld line performance of PP/Talc moldings produced in hot runner injection molds

AbstractWeld lines are weak regions in thermoplastic injection moldings caused by low molecular entanglement and unfavorable orientation. Their occurrence may lead to a significantly reduced mechanical performance of the products. Therefore, when weld lines are likely to occur in molded products, they must be taken into account during the mechanical and technological design processes. The weld lines become more critical when particulate fillers are compounded with the polymer. The performance of weld lines in talc‐filled polypropylene box moldings produced with a double‐gated hot runner mold is assessed in this work. The processing conditions were varied in order to cause morphology and tensile‐impact resistance changes. The weld performance at room temperature was assessed in terms of the energy absorbed in the impact tests. It was found that the performance depends on the injection temperature, the injection rate, and the orientation of the talc particles in the weld‐line plane. J. VINYL ADDIT. TECHNOL., 13:159–165, 2007. © 2007 Society of Plastics Engineers

Entanglement and the speed of evolution of multi-partite quantum systems

There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the ‘speed’ of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. Previous research done on this subject has been focused upon comparing extreme cases (highly entangled states versus separable states) or upon bi-partite systems. In the present contribution we explore the aforementioned connection (between entanglement and time evolution) in the cases of two-qubits and N-qubits systems, taking into account states of intermediate entanglement. In particular, we investigate a family of energetically symmetric states of low entanglement that saturate the quantum speed bound. We show that, as the number of qubits increases, very little entanglement is needed to reach the quantum speed limit.

Rheological properties of branched polystyrenes: linear viscoelastic behavior

Oscillatory shear measurements on a series of branched graft polystyrenes (PS) synthesized by the macromonomer technique are presented. The graft PS have similar molar masses (Mw between 1.3×105 g/mol and 2.4×105 g/mol) and a polydispersity Mw/Mn around 2. The molar masses of the grafted side chains Mw,br range from 6.8×103 g/mol to 5.8×104 g/mol, which are well below and above the critical entanglement molar mass Mc of linear polystyrene. The average number \({\ifmmode\expandafter\bar\else\expandafter\fi{p}}\) of side chains per molecule ranges from 0.6 to 6.7. The oscillatory measurements follow the time–temperature superposition principle. The shift factors do not depend on the number of branches. The zero-shear viscosities of all graft PS are lower than those of linear PS with the same molar mass, which can be attributed to the smaller coil size of the branched molecules. It is shown that the influence of branching on the frequency dependence of the dynamic moduli is weak for all graft PS that were investigated, which can be explained by the low entanglement density.

Rheological properties of branched polystyrenes: linear viscoelastic behavior

Oscillatory shear measurements on a series of branched graft polystyrenes (PS) synthesized by the macromonomer technique are presented. The graft PS have similar molar masses (M w between 1.3×105 g/mol and 2.4×105 g/mol) and a polydispersity M w /M n around 2. The molar masses of the grafted side chains M w,br range from 6.8×103 g/mol to 5.8×104 g/mol, which are well below and above the critical entanglement molar mass M c of linear polystyrene. The average number \({\ifmmode\expandafter\bar\else\expandafter\fi{p}}\) of side chains per molecule ranges from 0.6 to 6.7. The oscillatory measurements follow the time–temperature superposition principle. The shift factors do not depend on the number of branches. The zero-shear viscosities of all graft PS are lower than those of linear PS with the same molar mass, which can be attributed to the smaller coil size of the branched molecules. It is shown that the influence of branching on the frequency dependence of the dynamic moduli is weak for all graft PS that were investigated, which can be explained by the low entanglement density.