Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels

We study the multiplicativity of the output 2-norm for depolarized Werner-Holevo channels and show that multiplicativity holds for a product of two identical channels in this class. Moreover, it shown that the depolarized Werner-Holevo channels do not satisfy the entrywise positivity condition introduced by C. King and M.B. Ruskai, which suggests that the main result is non-trivial.Comment: 3 page

Quantization of Hall Conductance For Interacting Electrons on a Torus

We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e^2/h, up to exponentially small corrections in the linear size of the system. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.Comment: 28 pages, 4 figures, This paper significantly simplifies the proof and tightens the bounds previously shown in arXiv:0911.4706 by the same authors. Updated to reflect published versio

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\mathcal{H}$ into a tensor product of factors, we consider a class of "redundancy-constrained states" in $\mathcal{H}$ that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.Comment: 37 pages, 5 figures. Updated notation, references, and acknowledgemen

Entanglement in Finitely Correlated Spin States

We derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. Finitely correlated states are otherwise known as matrix product states or generalized valence-bond states. The bounds become exact in the limit of the entanglement of a single spin and the half-infinite chain to the right (or the left) of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient . Our result also generalizes the study of entanglement in the ground state of the AKLT model by Fan, Korepin, and Roychowdhury. Our result permits one to calculate more efficiently, numerically and in some cases even analytically, the entanglement of arbitrary finitely correlated quantum spin chains.Comment: PACS 03.67.Mn, 05.50.+q. Minor typos in v1 corrected. In v2: expanded Introduction and Discussion. Simplified proof of the main resul

Multipartite viruses: A decentralized mode of functioning. [O.24]

Multipartite viruses are characterized by a genome composed of two or more nucleic acid segments, each encapsidated indivually. A classical view in virology assumes that the viral replication cycle occurs within individual cells, where the whole viral genome information is replicated, and is then reiterated in successively infected cells during host invasion. In the context of multipartite viruses, this view implies that at least one copy of each of the genome segments must enter in each of the infected cells. The genome of the Faba bean necrotic stunt virus (FBNSV, Family Nanoviridae) is composed of 8 ssDNA circles of about 1000 bases, each encapsidated in an individual virus particle. We have previously shown that each of the eight segments reproducibly accumulates at a specific relative frequency, some representing around 30% of the total viral DNA within an infected plant and others not exceeding 2%. In this situation, it is difficult to conceive how FBNSV can actually transmit the whole genome information both from cell to cell and from host to host. If the segments enter cells indifferently, solely according to their frequency within the population, we could calculate that a successful infection of 95% of the susceptible cells would require the entry of nearly 200 particles per cell. This figure illustrates the enormous cost that FBNSV might bear at each cell-to-cell transmission step. Alternatively, this virus might infect individual cells with subgroups of genome segments, partial genome information being replicated at distinct location within a host. This may alleviate the cost at cell-to-cell passage but would imply a sort of unknown viral communication or complementation in between these subgroups of segments to maintain the integrity of the genome information. In any cases, the actual functioning of FBNSV is an enigma, because it is hard to conceive that a virus could force hundreds of particles in each newly colonized cells, or that the genome could function with separate subunits in distinct cells. We are currently developing tools to test the above alternatives. (Résumé d'auteur

Circulating virus load determines the size of bottlenecks in viral populations progressing within a host

For any organism, population size, and fluctuations thereof, are of primary importance in determining the forces driving its evolution. This is particularly true for viruses—rapidly evolving entities that form populations with transient and explosive expansions alternating with phases of migration, resulting in strong population bottlenecks and associated founder effects that increase genetic drift. A typical illustration of this pattern is the progression of viral disease within a eukaryotic host, where such demographic fluctuations are a key factor in the emergence of new variants with altered virulence. Viruses initiate replication in one or only a few infection foci, then move through the vasculature to seed secondary infection sites and so invade distant organs and tissues. Founder effects during this within-host colonization might depend on the concentration of infectious units accumulating and circulating in the vasculature, as this represents the infection dose reaching new organs or “territories”. Surprisingly, whether or not the easily measurable circulating (plasma) virus load directly drives the size of population bottlenecks during host colonization has not been documented in animal viruses, while in plants the virus load within the sap has never been estimated. Here, we address this important question by monitoring both the virus concentration flowing in host plant sap, and the number of viral genomes founding the population in each successive new leaf. Our results clearly indicate that the concentration of circulating viruses directly determines the size of bottlenecks, which hence controls founder effects and effective population size during disease progression within a host

Approximating the ground state of gapped quantum spin systems

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue

Persistence of locality in systems with power-law interactions

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.Comment: 5 pages, 4 figures, version accepted by PR

Area law for fixed points of rapidly mixing dissipative quantum systems

We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure, or the system is frustration free.Comment: 17 pages, 1 figure. Final versio